Combining Ground Penetrating Radar and a Terrestrial Laser Scanner to Constrain EM Velocity: A Novel Approach for Masonry Wall Characterization in Cultural Heritage Applications

Highlights

What are the main findings?

• Ground-Penetrating Radar (GPR) is a key method for cultural heritage investigation. Nevertheless, the absence of additional geophysical information can lead to severe uncertainties. The implementation of a methodology encompassing a geomatic approach has proven to be extremely suitable for GPR data processing.
• In cultural heritage, if both façades of a surveyed wall are accessible, a Terrestrial Laser Scanner (TLS) becomes extremely helpful to accurately estimate the wall’s thickness to be included in a customized GPR workflow.

What is the implication of the main finding?

• Thanks to the TLS, constraining the wall’s geometry allows a first-order estimation of 1D electromagnetic (EM) velocity to be used for a time-to-depth conversion of GPR data, once an interpretation of rear façade reflection is provided.
• Thanks to a well-constrained time-to-depth conversion, GPR’s radargram and the TLS’s point cloud were plotted together in the same workspace, facilitating straightforward visualization, interpretation, and comprehension for GPR non-experts as well.

Abstract

In this paper, the combined use of Ground Penetrating Radar (GPR) and a Terrestrial Laser Scanner (TLS) is illustrated to highlight multiple advantages arising from the integration of these two distinct Non-Destructive Testing (NDT) techniques in the investigation of a historical wall. In particular, thanks to the TLS point cloud, a precise evaluation of the medium’s thickness, as well as its irregularities, was carried out. Based on this accurate geometrical constraint, a first-order velocity model, to be used for a time-to-depth conversion and for a post-stack GPR data migration, was computed. Moreover, a joint visualization of both datasets (GPR and TLS) was achieved in a novel tridimensional workspace. This solution provided a more straightforward and efficient way of testing the reliability of the combined results, proving the efficiency of the proposed method in the estimation of a velocity model, especially in comparison to conventional GPR methods. This demonstrates how the integration of different remote sensing methodologies can yield a more solid interpretation, taking into account the uncertainties related to the geometrical irregularities of the external wall’s surface and the inner structure generating complex GPR signatures.

1. Introduction

Ground-Penetrating Radar (GPR) is an active-source geophysical method based on the propagation of electromagnetic (EM) waves according to the medium’s dielectric characteristics, as represented by the relative permittivity (${\epsilon }_r$) [1]. Due to its non-invasive nature, GPR can be applied to different fields, like geology [2,3], engineering [4], and cultural heritage [5,6,7]. GPR can be employed to characterize several features, such as the internal geometry of historical walls, possible structural defects (i.e., fractures and/or voids) [8,9,10], and areas chemically altered by moisture [11].

To correctly assess the EM properties of the studied media in relation to their internal characteristics, several processing steps are required. Among them, two of the most critical are depth conversion and migration [12], as they need an accurate velocity model, which might be very complicated to compute for heterogeneous media. To estimate EM velocity, various well-documented approaches are available in the scientific literature [1,13,14,15].

The propagation velocity of EM waves depends on the physical properties of the investigated media and, clearly, on their geometry and thickness. Generally, for conventional geological applications, an accurate definition of the thickness of layers might be a challenging problem, especially without any ground truthing.

On the other hand, while working on masonry structures, this problem may sometimes be partially addressed when, for instance, both sides of façades or walls of studied buildings are accessible [5,16]. This possibility plays a key role in the computation of the velocity of EM waves. Nevertheless, measuring the thickness of a historical wall using traditional techniques (e.g., surveying with metric tapes) is not sufficiently accurate and representative of the entire extent in delineating the average thickness, along with its local variations. In fact, such walls have been frequently reworked or rebuilt, for example, after destructive events like earthquakes. This fact may led to inaccurate values of the thickness, which, although of only a few centimeters, can strongly affect the accuracy of the estimation of the velocity model, as well as a more reliable qualitative and quantitative GPR interpretation.

An advanced approach to overcome this issue involves the integration of geomatic techniques, such as a survey with a Terrestrial Laser Scanner. Although a few papers have focused on similar goals [17], TLSs have been widely used to define the topographic surface for static correction in geological applications [18,19,20]. But the TLS and GPR integration reported in this study aims to obtain the following results:

• A high-resolution 3D visualization of the TLS’s surfaces, supporting a better understanding of the historical building’s geometry, irregularities, and structural characteristics;
• A more accurate reconstruction of the walls’ thickness, supporting the analysis and processing of GPR profiles by accurately constraining the EM velocity model and its local variations;
• An integrated 3D rendering of the building, setting up a workflow combining GPR profiles and TLS point clouds in the same platform;
• An accurate velocity model, demonstrating a strong correlation between velocity variations and the walls’ internal geometry and conservation state (e.g., voids and moisture content).

The proposed integrated approach was applied to a historical building, the Museo della Castellina in Norcia, sited in Central Italy (Figure 1). Built in the 16th century AD [21], this building has undergone several restorations and strengthening interventions due to seismic events that have occurred in the area over the centuries [22]. Even the last seismic sequence of 2016 caused significant damage conditions involving all the structure, especially on the northern sector, which required important restoration works. In this context, this research is contextualized in the use of a methodology allowing the improvement of the knowledge of the constituent materials. In particular, the survey was conducted over the façade of the ex “Palazzo del Podestà”, an older building partially demolished and later embedded inside the Museo della Castellina structure, preserving its original orientation [23], as will be shown in the next chapter.

2. Materials and Methods

2.1. Laser Scanner Survey

A laser scanning survey was conducted using the Terrestrial Laser Scanner “Faro Focus 3D” (Faro) instrumentation [25], covering an angular range of 360° horizontally and from −60° to 90° vertically. A total of forty-three color-enhanced scans were acquired with a resolution of approximately 7.5 mm at a 10-m distance and a duration of about nine minutes for each scan. The survey covered both exterior and interior areas, including the ground floor—where the wall under investigation is located—and the first floor, to obtain a comprehensive point cloud suitable for further analyses. Specifically, seven scans were conducted in the exterior areas, nineteen in the ground-floor interiors, and seventeen on the first floor (Figure 2).

Spherical and checkerboard targets were strategically positioned within the surveyed areas to support post-processing, enabling the accurate registration and merging of individual scans into a unified point cloud (Figure 3).

The positions of the checkerboard targets placed on the ground in the external San Benedetto Square were measured using geodetic GNSS (Global Navigation Satellite System) receivers operating in Network Real-Time Kinematic (NRTK) mode, enabling the georeferencing of the entire survey within the global Datum ETRF2000. The analyses focused on the internal wall were carried out on a 3D model, later referenced in a local coordinate system rigidly aligned with the wall, to simplify the integration with GPR datasets.

TLS data were processed using Faro Scene software v. 2021.4.0 (Faro) [26], yielding a maximum registration error of less than 0.013 m at the target and sphere positions with an average error of 0.004 m. The unified point cloud consists of approximately 880 million points.

To extract and analyze the geometry of the wall under investigation, the point clouds generated through the TLS were further processed using Leica Cyclone software (v. 2021.1.2) [27] (Figure 4).

From the overall point cloud, the wall under investigation was extracted and subjected to a rigid transformation (rotation and translation) to align it with the coordinate system used for the GPR analyses. In this new reference frame, the X-axis was aligned along the wall, the Y-axis oriented vertically upwards, and the Z-axis directed along the thickness of the wall (Figure 5).

2.2. GPR Survey

To study the above-mentioned portion of the wall, 14 profiles were acquired in a Common Offset (CO) configuration following a pseudo-regular grid, with adaption during the fieldwork to limit possible poor antenna–wall coupling due to the irregular texture of the wall surface (Figure 6). In particular, the horizontal profiles were collected for increasing Y along the Y-axis, while vertical ones were collected for increasing X along the X-axis (

Table 1. Table summarizing surveyed GPR profiles. As for the horizontal profiles (from P1 to P6), the “Distance (m)” column refers to the vertical distance (i.e., height) along the Y-axis. Instead, as for the vertical profiles (from P7 to P14), the “Distance (m)” column refers to the horizontal distance along the X-axis. All the geometrical information provided refers to the Cartesian coordinate system shown in Figure 6.

Profile Name	Length (m)	Distance (m)
P1	4.22	0.25
P2	4.05	0.6
P3	4.05	1.15
P4	4.12	1.6
P5	4.02	2.1
P6	4.22	2.3
P7	2.84	0.15
P8	3.07	0.65
P9	2.97	1
P10	3.2	1.5
P11	3.23	2
P12	3.36	2.5
P13	3.37	2.9
P14	3.31	3.5

). Measurements were carried out using a Zond-12e Advanced GPR system, equipped with a 1.5 GHz antenna, selected due to its centimetric resolution capability, small size, and embedded odometer, making it ideal for this application. Survey parameters are detailed in

Table 2. GPR survey parameters used during the fieldwork.

Survey Parameters	Numerical Parameters
Antenna Central Frequency (GHz)	1.5
Source–Receiver offset (m)	0.13
Samples per traces	1024
Time window (ns)	50
Sampling frequency (GHz)	10
Trace inter-distance (m)	0.01

.

2.3. GPR Data Processing

The raw GPR data were processed to enhance the signal-to-noise (S/N) ratio and compensate for the amplitude decay of the reflected events [5]. After several tests, the following processing steps were applied to GPR data using ReflexW commercial software [29]: static correction; trace editing; Dewow; background removal; averaging filter; bandpass filter; and amplitude recovery (

Table 3. Example of processing flow applied to GPR profile “P5”.

Survey Parameters	Numerical Parameters
Static correction	-
Trace editing	-
Dewow filter	Window: 1.15 ns
Background removal	Trace window: 0.3–25 ns
Averaging filter	Number of samples: 3 Number of traces: 3
Butterworth bandpass filter (MHz)	Cutoff frequencies: 400–1350
Amplitude recovery	Time window (ns): 0.3–25 Linear gain: 0.05 Exponential gain: 1.2 Maximum gain: 1000

). Results of this processing flow are shown in Figure 7.

2.4. GPR-TLS Data Integration

The TLS can support GPR data acquisition and interpretation to achieve different goals, such as the definition of the topography for static corrections [18,19,20] and the evaluation of surfaces, both geological [30] and anthropic [31,32]. For cultural heritage applications, the TLS is generally used as an additional NDT method to GPR with the aim of monitoring structures [33,34] or providing an accurate 3D model [35]. Nevertheless, the employment of the TLS for other purposes, like tuning an EM velocity model [15] or achieving, on a unique platform, a joint visualization to improve data interpretation [35], has not really been addressed yet. In this paper, such integration is investigated and proposed. The first step is to accomplish the visualization of both TLS and GPR data in the same spatial environment by using the software CloudCompare [28]. More specifically, the first necessary operation is the definition of a Cartesian axis orientation that, for this work, was agreed following preliminary tests. Subsequently, for TLS data, final point clouds were re-oriented according to the new local reference system. After assigning coordinates to processed GPR radargrams accordingly, they were exported from the original SEG-Y format to ASCII format via ReflexW and finally imported into CloudCompare (Figure 8). ASCII files have been set up and organized in 4 columns: X-coordinates; Y-coordinates; Z-coordinates; and trace amplitude.

3. Results

3.1. EM Velocity Modeling—Synthetic Scenario

The travel time of EM waves is controlled by the combination of both physical (e.g., relative permittivity) and geometrical (e.g., thickness) properties of the medium. By precisely constraining at least one of such quantities, it is possible to achieve a more accurate estimation of the EM waves’ velocity, aiding the extrapolation of information about the internal walls’ structure and heterogeneities. The use of GPR modeling can help the prediction of a given recorded event by quantifying how much the variation in one specific parameter can affect the arrival time of the same event. To simulate EM wave propagations, Maxwell’s laws are generally solved in the time domain using a Finite-Difference Time-Domain (FDTD) approach [36], which requires a proper spatio-temporal discretization of the model [37]. This represents a crucial step, since, as stated by the Courant–Freidrichs–Lewy (CFL) condition [38], dimensions assigned to the model’s cells affect time steps. Several examples of GPR modeling applied to geology [39,40,41], engineering [42,43], and cultural heritage [44,45] are available in the literature, using both commercial and open-source software (e.g., gprMax [46] and ReflexW [29]).

In Figure 9, two homogeneous media A and B with the same thickness Z ($Z_A$ = $Z_B$ = 1 m) and different relative permittivities (${ϵ}_{\mathrm{rA}}$ = 4 and ${ϵ}_{\mathrm{rB}}$ = 6) are considered (Table 4 and Table 5). Since the velocity of propagation in low-loss media is inversely proportional to the square root of the relative permittivity [1], the two-way travel time (TWT) associated with the reflection in medium A ($TW{T}_A$) will be lower than in the case of medium B ($TW{T}_B$). Conversely, in Figure 10, the results obtained in two homogeneous media A and B with the same relative permittivity (${ϵ}_{\mathrm{rA}}$ = ${ϵ}_{\mathrm{rB}}$ = 6) but different thicknesses ($Z_A$ = 1 m and $Z_B$ = 1.2 m) are shown (Table 6 and Table 7). In this case, since the waves propagate over a wider distance for medium B, $TW{T}_B$ is higher than $TW{T}_A$.

The possibility of constraining at least one of the two factors is very significant for the well-known non-uniqueness of the solution affecting the inverse problem in geophysical methods [47]. In Figure 11, an example of this condition is provided (Table 8 and Table 9) by considering two media A and B with different relative permittivities (${ϵ}_{\mathrm{rA}}$ = 4 and ${ϵ}_{\mathrm{rB}}$ = 6) and thicknesses ($Z_A$ = 1.8 m and $Z_B$ = 1.47 m). The ambiguity in the prediction of the recorded two-way travel time in a simple model shown is, clearly, worse in the case of a real experimental scenario due to the common logistical difficulties during field surveying (e.g., accessibility to the site, and local obstacles), the variation in the target geometries (i.e., surface roughness and thickness discrepancies), and the internal heterogeneities of a masonry wall (e.g., material variation as well as the presence of voids and/or fractures). All these conditions inevitably produce velocity changes that deviate from a purely 1-D model.

Table 4. Model parameters for Figure 9.

Survey Parameters	Numerical Paramaters
	Medium A	Medium B
Thickness (m)	1	1
Length (m)	3.5	3.5
Relative permittivity	4	6
Electrical conductivity (S/m)	0	0

Table 4. Model parameters for Figure 9.

Survey Parameters	Numerical Paramaters
	Medium A	Medium B
Thickness (m)	1	1
Length (m)	3.5	3.5
Relative permittivity	4	6
Electrical conductivity (S/m)	0	0

Table 5. Simulation parameters for Figure 9.

Simulation Parameters	Numerical Parameters
Domain (m)	3.5 × 1.2 × 0.002
Spatial discretization (m)	0.002
Time window (ns)	50
Waveform	Ricker
Source	Hertzian Dipole
Nominal frequency (GHz)	1
Tx-Rx offset (m)	0.13

Table 5. Simulation parameters for Figure 9.

Simulation Parameters	Numerical Parameters
Domain (m)	3.5 × 1.2 × 0.002
Spatial discretization (m)	0.002
Time window (ns)	50
Waveform	Ricker
Source	Hertzian Dipole
Nominal frequency (GHz)	1
Tx-Rx offset (m)	0.13

Figure 9. In (a), media A and B are shown via Paraview [48]. From a geometrical point of view, they are identical, while they have different relative permittivities. In (b), the two respective synthetic traces—computed by simulating the EM wave propagation via gprMax [46] and replotted via Matlab [49]—are shown. The source and receiver are located along the top air–wall interface; therefore the backside wall’s reflection is caused by the bottom wall–air interface. The polarity of this signal (black dashed box) is in phase with the direct arrivals (red dashed box) as the reflection coefficient is positive [50].

Figure 9. In (a), media A and B are shown via Paraview [48]. From a geometrical point of view, they are identical, while they have different relative permittivities. In (b), the two respective synthetic traces—computed by simulating the EM wave propagation via gprMax [46] and replotted via Matlab [49]—are shown. The source and receiver are located along the top air–wall interface; therefore the backside wall’s reflection is caused by the bottom wall–air interface. The polarity of this signal (black dashed box) is in phase with the direct arrivals (red dashed box) as the reflection coefficient is positive [50].

Table 6. Model parameters for Figure 10.

Survey Parameters	Numerical Paramaters
	Medium A	Medium B
Thickness (m)	1	1.2
Length (m)	3.5	3.5
Relative permittivity	6	6
Electrical conductivity (S/m)	0	0

Table 6. Model parameters for Figure 10.

Survey Parameters	Numerical Paramaters
	Medium A	Medium B
Thickness (m)	1	1.2
Length (m)	3.5	3.5
Relative permittivity	6	6
Electrical conductivity (S/m)	0	0

Table 7. Simulation parameters for Figure 10.

Survey Parameters	Numerical Paramaters
	Medium A	Medium B
Domain (m)	3.5 × 1.2 × 0.002	3.5 × 1.4 × 0.002
Spatial discretization (m)	0.002
Time window (ns)	50
Waveform	Ricker
Source	Hertzian Dipole
Nominal frequency (GHz)	1
Tx-Rx offset (m)	0.13

Table 7. Simulation parameters for Figure 10.

Survey Parameters	Numerical Paramaters
	Medium A	Medium B
Domain (m)	3.5 × 1.2 × 0.002	3.5 × 1.4 × 0.002
Spatial discretization (m)	0.002
Time window (ns)	50
Waveform	Ricker
Source	Hertzian Dipole
Nominal frequency (GHz)	1
Tx-Rx offset (m)	0.13

Figure 10. In (a), media A and B are shown. From an electromagnetic point of view, they are identical as they share the same relative permittivity, while they have different thicknesses. In (b), the two synthetic traces are shown. The source and receiver are located along the top air–wall interface; therefore the backside wall’s reflection is caused by the bottom wall–air interface. The polarity of this signal (black dashed box) is in phase with the direct arrivals (red dashed box) as the reflection coefficient is positive [50].

Figure 10. In (a), media A and B are shown. From an electromagnetic point of view, they are identical as they share the same relative permittivity, while they have different thicknesses. In (b), the two synthetic traces are shown. The source and receiver are located along the top air–wall interface; therefore the backside wall’s reflection is caused by the bottom wall–air interface. The polarity of this signal (black dashed box) is in phase with the direct arrivals (red dashed box) as the reflection coefficient is positive [50].

Table 8. Model Parameters for Figure 11.

Survey Parameters	Numerical Paramaters
	Medium A	Medium B
Thickness (m)	1.8	1.47
Length (m)	3.5	3.5
Relative permittivity	4	6
Electrical conductivity (S/m)	0	0

Table 8. Model Parameters for Figure 11.

Survey Parameters	Numerical Paramaters
	Medium A	Medium B
Thickness (m)	1.8	1.47
Length (m)	3.5	3.5
Relative permittivity	4	6
Electrical conductivity (S/m)	0	0

Table 9. Simulation parameters for Figure 11.

Survey Parameters	Numerical Paramaters
	Medium A	Medium B
Domain (m)	3.5 × 2 × 0.002	3.5 × 1.67 × 0.002
Spatial discretization (m)	0.002
Time window (ns)	50
Waveform	Ricker
Source	Hertzian Dipole
Nominal frequency (GHz)	1
Tx-Rx offset (m)	0.13

Table 9. Simulation parameters for Figure 11.

Survey Parameters	Numerical Paramaters
	Medium A	Medium B
Domain (m)	3.5 × 2 × 0.002	3.5 × 1.67 × 0.002
Spatial discretization (m)	0.002
Time window (ns)	50
Waveform	Ricker
Source	Hertzian Dipole
Nominal frequency (GHz)	1
Tx-Rx offset (m)	0.13

Figure 11. In (a), media A and B with different relative permittivities and thicknesses are shown. In (b), the two synthetic traces are shown. The source and receiver are located along the top air–wall interface; therefore the backside wall’s reflection is caused by the bottom wall–air interface. Despite the media’s differences, the rear façade reflections (aligned between black dashed lines) occur at the same time but differ in terms of amplitude since the reflection coefficients (RCs) are different ($R{C}_B$ > $R{C}_A$) [50]. Lastly, the polarity of the reflected signals (black dashed lines) is in phase with the direct arrivals (red dashed box) as the reflection coefficient is positive [50].

Figure 11. In (a), media A and B with different relative permittivities and thicknesses are shown. In (b), the two synthetic traces are shown. The source and receiver are located along the top air–wall interface; therefore the backside wall’s reflection is caused by the bottom wall–air interface. Despite the media’s differences, the rear façade reflections (aligned between black dashed lines) occur at the same time but differ in terms of amplitude since the reflection coefficients (RCs) are different ($R{C}_B$ > $R{C}_A$) [50]. Lastly, the polarity of the reflected signals (black dashed lines) is in phase with the direct arrivals (red dashed box) as the reflection coefficient is positive [50].

3.2. Constraining Thickness

In the presented case study, the accessibility of both front-side and back-side façades granted the possibility to give an accurate estimation of the medium’s thickness.

The first attempt at reconstructing the wall’s thickness was made through a direct survey by using a meter tape (MT). After several measurements, an average estimation of 1.08 ± 0.02 m (where ±0.02 is the standard deviation of all the measurements’ values) was achieved. It is important to underline that, by using this approach, multiple types of errors can add up due to several factors, like possible wrong tape positioning by field operators, non-repeatability of measurements, and the presence of protruding columns that border the wall, making such process not as straightforward as they might seem.

Therefore, to constrain the wall’s geometry, overcoming all these uncertainties, the TLS was employed to extract such parameters with high accuracy. Firstly, the coordinates over both sides of the wall were extracted from the TLS’s point cloud along GPR surveying profiles using CloudCompare v2.13.2’s Cross Section tool. In the case of the selected GPR profile, the thickness across the wall’s section is essentially homogeneous. Such a condition is not always true across the entire wall’s height. For example, profile P3 (Y = 1.15 m) shows remarkable variations along the Z-axis (Figure 12), making the geometry of the medium non-uniform.

Hence, the thickness can be indirectly estimated by considering the linear distance along the Z-axis for each pair of points (i.e., for each set of points placed, respectively, on the front and the back façades and sharing the same X-coordinate). However, it is crucial to consider that the TLS always acquires points randomly spaced, depending on both scanner-to-wall distance and the number of the scans. For this reason, the total number of points collected on the façades crossing the P5 profile is different: 645 points for the front façade (FF) and 578 points for the rear façade (RF), with a spatial sampling frequency of, roughly, 184 and 165 points/meter, respectively. This difference is not only numerical but also spatial inasmuch as, for example, the first five X-coordinates of FF’s points are 0, 0.004, 0.008, 0.015, and 0.02, while RF’s ones are 0, 0.002, 0.005, 0.007, and 0.01, where 0 matches with the beginning X-coordinate of P5. Consequently, before thickness’s extraction, X and Z coordinates were recomputed to account for this issue, as summarized by the following list and graphical sketch (Figure 13):

• A univocal X coordinate dataset is defined by merging together the X coordinates of the two datasets (FF and RF) and removing duplicated points so that each X coordinate is present only once in the final dataset;
• FF’s and RF’s X coordinates are replaced with the new dataset (ND) defined in the previous step;
• Since the ND is bigger than the previous datasets in terms of X coordinates, several points of this dataset have no Z coordinates. To account for this, missing Z coordinates were computed via 1D linear interpolation;
• Thickness estimation (T) was performed by subtracting, for each X-coordinate, the corresponding Z-coordinate for the entire set of points.

3.3. GPR-TLS Joint Visualization

EM velocity is useful for multiple objectives, like time–depth conversion (which represents the last processing step performed to achieve TLS-GPR joint visualization) and post-stack migration, which will be better addressed later. In particular, the main aim of depth conversion is to convert the radargram’s vertical axis from the TWT domain (i.e., from the time domain) to the space domain to correlate the observed GPR echoes with their probable depth. From a mathematical point of view, time-to-depth conversion is a scaling operation of a variable (i.e., TWT) by a constant value (i.e., EM velocity, which, in this case, is equal to 0.112 m/ns). Therefore, the geometrical features of the signal remain unaltered after applying this step.

Figure 13. Graphical sketch of the previous list. Numbers 1–4 correspond to the bullet points.

Figure 13. Graphical sketch of the previous list. Numbers 1–4 correspond to the bullet points.

To start with a simple approach, EM velocity can be calculated by considering the average thickness of the wall. Using this constraint, conventional 1D GPR forward modeling can aid the comprehension of the prominent reflection generated from the backside wall. Its TWT can be easily predicted and then picked out of surveyed data. This procedure allows the estimation of the average velocity of the medium using the same approach used for Earth science applications upon the availability of the stratigraphic tops of the reflections [51]. In Figure 14, the reflection (picked out with a red polyline) interpreted as the rear wall’s façade is shown. In particular, following the TWTs predicted by 1D simulations, and the observation of all the deepest relevant GPR signals, such an event shows the highest lateral continuity despite being slightly variable in the time domain. In this case, the picked reflection in Figure 14 seems to have preserved the same polarity (peak–trough–peak) as direct arrivals (Figure 15). This condition is in agreement with the expected positive reflection coefficient [50] caused by the electromagnetic interface between the wall and the air.

So, considering an average TWT of 17.3 ± 0.6 ns, a 1D EM velocity of 0.112 ± 0.005 m/ns was computed using the thickness defined with the TLS. In this way, the wall’s relative permittivity was calculated using the formula for EM velocity in a low-loss environment (Equation (1)).

$$V_{\mathrm{EM}} \approx {\displaystyle \frac{c}{\sqrt{{\epsilon }_r}}} \iff {\epsilon }_r \approx {\left({\displaystyle \frac{c}{v_{\mathrm{em}}}}\right)}^2 \approx 7.15 \pm 0.01$$

(1)

where “$V_{EM}$” is the velocity for EM waves; “c” the velocity of light in vacuum; and “${ϵ}_{\mathit{r}}$” the relative permittivity.

In particular, the computed relative permittivity overlaps with the typical range of carbonate rocks (${ϵ}_{\mathit{r}}$ = 4–8), which can be attributed to the materials forming the wall [1]. It is important to point out that, by using the MT approach, a $V_{EM}$ of 0.125 ± 0.007 m/ns—with a corresponding ${ϵ}_{\mathit{r}}$ of 5.79 ± 0.04—would have been calculated. Since this value of relative permittivity falls, once again, within the range typical of carbonate rocks, such an erroneous result would have been arduous to spot without the support of the TLS. Obviously, since a $V_{EM}$ of 0.125 ± 0.007 m/ns is higher, the average rear façade reflection would have occurred earlier in the time domain. Equation (1) can be rearranged in Equation (2) to solve for two-way travel time TWT.

$$V_{\mathrm{EM}} = {\displaystyle \frac{s}{t}} = {\displaystyle \frac{2s}{\mathrm{TWT}}} \approx {\displaystyle \frac{c}{\sqrt{{\epsilon }_r}}} {\displaystyle \iff } \mathrm{TWT} \approx {\displaystyle \frac{2s\sqrt{{\epsilon }_r}}{c}} \approx 15.6 \pm 0.6\mathrm{ns}$$

(2)

Here “$V_{EM}$” is the velocity for EM waves; “s” is the space (i.e., TLS’s average thickness); t is the one-way travel time; TWT is the two-way travel time; “c” is the velocity of light in vacuum; and “${ϵ}_{\mathrm{r}}$” is the relative permittivity.

In this way, the rear façade reflection should have occurred, on average, 1.7 ns earlier than the real case. This error is remarkable considering that the estimation of the wall’s thickness was achieved with two different methods (meter tape and Terrestrial Laser Scanner). This result neatly shows how supplementary uncertainties accumulate alongside those typical of indirect methodologies such as GPR. This condition can produce greater inaccuracies if thickness variations occur throughout the GPR profile, as shown in Figure 12.

Finally, the P5 profile was depth-converted using the TLS’s 1D velocity model (Figure 16) and imported into CloudCompare (Figure 17) using the workflow of Figure 8.

As stated before, a velocity model can be used for data migration. Conversely to depth conversion, migration algorithms are used to improve the imaging of a radargram by reconstructing the distribution of the reflectivity and restoring the true location of targets [52]. This is mainly achieved by collapsing scattered energy into its source point and restoring the true dip angle for non-horizontal reflectors [1]. Although post-stack time migration techniques are strongly influenced by the quality of field velocity estimation and based on assumptions that generally do not match real case scenarios (e.g., spherical propagation of the source, monostatic data collection, and absence of lateral velocity contrast), this processing step is widely adopted to improve GPR interpretation [5,8,53,54,55,56]. Using the two 1D velocity models (MT’s and TLS’s ones), the P5 GPR profile was time-migrated with a diffraction stack algorithm (Figure 18).

3.4. Two-Dimensional EM Velocity Modeling—Experimental Scenario

Although the investigated thickness is highly homogeneous (0.973 ± 0.008 m), the reflection is still not flat, highlighting the inner dialectical heterogeneities within the surveyed medium. Therefore, by the TLS constraint of thickness, a 1D relative permittivity model was computed to account for this condition. More specifically, from the ratio between the thickness and the TWTs picked for each trace, a starting velocity model was calculated. In particular, $V_{EM}$ varies between 0.104 and 0.119 m/ns, with an average value of 0.112 m/ns. The reliability of such results was successfully tested by a simulation in gprMax (Figure 19) accomplished after the following steps:

• Conversion from velocity to relative permittivity, with the latter being the input required by the software;
• Discretization of the model by assigning to each centimetre (i.e., to each trace) the correspondent values of relative permittivity (Table 10 and Table 11).

In conclusion, EM waves propagates faster in the portions of the medium with ${ϵ}_{\mathrm{r}}$ lower than 7.15 and slower in the ones showing a greater value of ${ϵ}_{\mathrm{r}}$.

Table 10. Simulation parameters for Figure 19.

Simulation Parameters	Numerical Parameters
Domain (m)	3.5 × 1.17 × 0.002
Spatial discretization (m)	0.002
Time window (ns)	25
Waveform	Ricker
Source	Hertzian Dipole
Nominal frequency (GHz)	1
Tx-Rx offset (m)	0.13
Number of traces	351

Table 10. Simulation parameters for Figure 19.

Simulation Parameters	Numerical Parameters
Domain (m)	3.5 × 1.17 × 0.002
Spatial discretization (m)	0.002
Time window (ns)	25
Waveform	Ricker
Source	Hertzian Dipole
Nominal frequency (GHz)	1
Tx-Rx offset (m)	0.13
Number of traces	351

Table 11. Model parameters for Figure 19.

Survey Parameters	Numerical Paramaters
Thickness (m)	0.97
Length (m)	3.5
Relative permittivity	1 for Air, [6.31, 8.33] for Wall
Electrical conductivity (S/m)	0

Table 11. Model parameters for Figure 19.

Survey Parameters	Numerical Paramaters
Thickness (m)	0.97
Length (m)	3.5
Relative permittivity	1 for Air, [6.31, 8.33] for Wall
Electrical conductivity (S/m)	0

Figure 18. In (a,b), yjr P5 profile is migrated using, respectively, constant velocities of 0.112 m/ns and 0.125 m/ns derived from the laser scanner and meter tape thickness measurements. In both cases, a diffraction stack migration algorithm has been applied to the entire profile by summing 30 traces. Moreover, even though several reflections (included the rear façade one) seem to have been flattened properly, some typical migration artifacts can be observed in the upper portion of the radargram. In particular, undermigrated (yellow rectangles) and overmigrated (red rectangles) hyperbola are present, suggesting possible velocity variations due to the wall’s heterogeneities.

Figure 18. In (a,b), yjr P5 profile is migrated using, respectively, constant velocities of 0.112 m/ns and 0.125 m/ns derived from the laser scanner and meter tape thickness measurements. In both cases, a diffraction stack migration algorithm has been applied to the entire profile by summing 30 traces. Moreover, even though several reflections (included the rear façade one) seem to have been flattened properly, some typical migration artifacts can be observed in the upper portion of the radargram. In particular, undermigrated (yellow rectangles) and overmigrated (red rectangles) hyperbola are present, suggesting possible velocity variations due to the wall’s heterogeneities.

Figure 19. In (a), the model computed to run the simulation is shown. The source and receiver are located along the top air–wall interface; therefore the backside wall’s reflection is caused by the bottom wall–air interface, while its polarity (yellow dashed box) is in phase with the direct arrivals (red dashed box) as the reflection coefficient is positive [50]. In (b), the synthetic radargram after applying a constant time drift removal of 1.3 ns is shown. Vertical exaggeration: ×2.

Figure 19. In (a), the model computed to run the simulation is shown. The source and receiver are located along the top air–wall interface; therefore the backside wall’s reflection is caused by the bottom wall–air interface, while its polarity (yellow dashed box) is in phase with the direct arrivals (red dashed box) as the reflection coefficient is positive [50]. In (b), the synthetic radargram after applying a constant time drift removal of 1.3 ns is shown. Vertical exaggeration: ×2.

4. Discussions

The TLS can provide a strong support for GPR for different purposes, such as topographic mapping [18,19,20] and anthropic surface evaluation [33,34,35] in cultural heritage applications. Another possibility relies on the accessibility of the geomatic equipment on both surfaces for a given medium. In such cases, it is possible to define the investigated thickness with a TLS and, by combining this information with the EM reflection associated with the opposite surface, to compute EM velocity accordingly. A similar application has already been exploited in the scientific literature for cavity characterization [17].

However, although these acquisition techniques are based on different methodological principia, a full integration and visualization of such datasets may be extremely advantageous for several reasons, like validating different survey results and facilitating a joint interpretation.

For example, thanks to the TLS, starting from the accurate definition of the wall thickness and its variations, it has been possible to achieve the following:

• Significantly refine conventional measures obtained with the meter tape, thereby eliminating—or, at least, strongly reducing—any potential inaccuracy introduced by field operations;
• Use this information as a geometric constraint to define EM velocity models, after providing an interpretation of the backside wall reflection.

As stated in the previous chapter, the definition of a velocity model is necessary for two different processing steps: time–depth conversion and migration. In the first case, since the geometrical features of the signals are not modified, the shape of the rear façade reflection can be indicative of possible electromagnetic heterogeneities characterizing the studied medium. So, since construction blocks should probably be made of limestones belonging to Umbria–Marche Stratigraphic Succession (e.g., “Scaglia Rossa” or “Maiolica” formations) [57,58], the dominant factor influencing TWTs may be the presence of air associated with heterogeneous discontinuities among the blocks. This interpretation is based on the observation that, as shown by the TLS, the variations in the wall’s thickness might be considered negligible, thus making the relative permittivity the main factor controlling the TWTs of the rear façade reflection. This deduction may appear trivial only because of the dual integration (both graphical and methodological) achieved for the two datasets.

Conversely, post-stack time migration artifacts suggest that the 1D velocity model used is not sufficiently tuned to collapse all the hyperbolic diffractions. This condition, caused by the heterogeneities within the masonry wall, is supported by the presence of migration smiles and migration frowns, denoting how the selected velocity is, respectively, too high or too low. In future works, these inaccuracies will be addressed using a 2D velocity model to be possibly built also using multi-offset acquisition configurations and processing methodologies (e.g., semblance analysis).

The main drawback regarding this integration is that, to acquire point clouds over wide surfaces, TLS acquisitions may be time-consuming. Moreover, during TLS measurements, since no physical obstacles between the target (i.e., surfaces) and instrument can be introduced, the same target cannot be simultaneously surveyed with GPR. These conditions require a careful field logistic plan, aimed to synchronize both methods’ surveys so that time, space, and field efforts can be optimized. Another potential issue concerns the interpretation of the backside wall’s reflection, as this event might have a low signal-to-noise ratio and continuity. In this occurrence, the picking of the event risks is excessively subjective. To make the reflection’s strength more distinct, a well-documented solution in the scientific literature relies on placing a metal plate on the wall’s backside [59,60,61,62], obviously taking care to avoid any damage to the studied medium.

Despite of the aforementioned limitations, this research opens up the use of advanced GPR acquisition configurations and processing algorithms, as well as complementary geophysical methods (i.e., ERT). More specifically, the latter will be carried out with special focus on the portions that might present EM patterns associated with mechanical degradation (e.g., phase shift caused by voids [50]), aiming to address in a more detailed way the state of conservation of the wall.

Finally, the benefits of performing this joint analysis can be extremely advantageous to straightforwardly locate the interpreted EM features inside the studied medium (e.g., block distribution and/or altered area), correlating them with the external characteristics, such as thickness variation or surface roughness of the wall.

5. Conclusions

In this paper, a multi-sensing approach based on the combined use of GPR and a TLS was proposed to obtain more reliable results in the application of the GPR technique on masonry walls. An experimental campaign was carried out at the Museo della Castellina in Norcia (Central Italy) in light of its restoration due to the damage that occurred after the 2016–2017 earthquakes. The necessity to restore and preserve historical buildings cannot disregard a proper geophysical characterization, allowing the understanding of the internal geometrical properties of the analyzed structure. To achieve this, shrewd data processing and interpretation is required. Nevertheless, the lack of additional geophysical information can make the hardest processing steps even more challenging, like in the case of EM velocity estimation. Therefore, extracting helpful constraints from non-geophysical methods may play a key role in the refinement of the data analysis process to clarify interpretative aspects.

For these reasons, GPR data were combined with TLS data. This integrated approach has yielded various pros in terms of GPR data processing, since this geomatic technique allows for several advantages, such as the evaluation of surfaces’ roughness and the definition of the wall’s thickness variation with millimetric accuracy. A significant refinement of the estimation of the medium’s geometrical properties, in comparison to traditional methods, was achieved. In addition, together with the rear façade reflection’s interpretation, a first-order, accurate 1D average velocity model used for depth conversion and time migration was calculated.

These processing steps were useful for two different purposes: the former to perform a visual integration between the TLS’s point cloud and P5 GPR profile, since, to display the datasets together, X-Y-Z coordinates must be defined in the same unit (i.e., meter). Moreover, the provided joint data visualization, achieved in a novel way after defining a customized workflow, has granted several advantages. Firstly, results are shown in the same workspace, allowing for a combined visualization of both datasets. Secondly, it is possible to make important geophysical inferences in the interpretation process.

Hence, the velocity model proved to be helpful to study the rear reflection in terms of relative permittivity variations, but improvements are surely needed to cope with the internal heterogeneities that have not been modeled yet.

In conclusion, in the light of the lack of additional geophysical methods, the TLS has proven to be a powerful technique to extract helpful information for GPR data processing and EM feature interpretation. In this way, an accurate refinement of the thickness of the studied wall and an evaluation of the influence of its geometry over surveyed GPR data were carried out.