ORIGINAL RESEARCH OR TREATMENT PAPER

High-Resolution Ultrasonic Imaging of Artworks with Seismic Interferometry forTheir Conservation and RestorationDeyan Draganov 1, Jürg Hunziker1,2, Karel Heller1, Karin Gutkowski3 and Fernando Marte4

1Department of Geoscience and Engineering, Delft University of Technology, Delft, Netherlands; 2Faculté des géosciences et del’environnement, Institut des sciences de la Terre – ISTE, Université de Lausanne, Lausanne, Switzerland; 3Comisión Nacional de EnergíaAtómica, Buenos Aires, Argentina; 4Instituto de Investigaciones sobre el Patrimonio Cultural, Universidad Nacional de San Martín, SanMartín, Argentina

ABSTRACTArtworks are an inseparable part of the cultural heritage of societies and provide us with aunique look at cultural developments through time and space. For the best possibleconservation, it is paramount to know the constituent materials, condition, and constructiontechniques of the objects (e.g. painting on wood, fresco, sculpture). Such information isrequired not only for the surfaces of the objects, but also for the interiors; in the imagingdiscipline, this is known as depth imaging. Here, we introduce a new method for non-invasive depth imaging as an alternative to traditional non-invasive methods when the lattercannot be used to obtain the required information. We use ultrasonic transverse-wavetransmission measurements and turn them into virtual reflection measurements. We achievethis by applying seismic interferometry with active sources. Obtaining reflectionmeasurements by seismic interferometry allows us to apply an advanced imaging technique– prestack depth migration, as used in seismic exploration – to produce a high-resolutiondepth image of an object. We apply our method to ultrasonic data recorded on a mockup ofa painting on a wooden support. We validate our method by comparing our results with animage from X-ray computed tomography.

ARTICLE HISTORYReceived April 2016Accepted February 2018

KEYWORDSSeismic interferometry;transverse waves; ultrasonic;imaging; artefacts; artworks;conservation; restoration

Introduction

The inter disciplinary activity of art conservation aims atgenerating knowledge about objects (e.g. structureand history), understanding the deterioration pro-cesses of their materials, and implementing methodsfor adequate conservation and restoration.

A principal criterion governing conservation isminimum intervention, which seriously restricts theapplicable examination techniques. An importantorientation in sciences like physics and chemistry isthe development of non-invasive techniques (Milianiet al. 2010) sensitive to different phenomena. Examin-ation of paintings on wood (Figure 1(a)), wall paintings,and sculptures employs mainly techniques to analysean object’s surface. To see deeper inside an object,techniques like ultraviolet-induced luminescence pho-tography (Taft and Mayer 2000), infrared reflectogra-phy (Pezzati, Materazzi, and Poggi 2004; Daffara,Fontana, and Pezzati 2009), X-ray radiography(Mottin, Martin, and Laval 2007), and X-ray computedtomography (Casali and Bettuzzi 2009) (CT) havebeen used. Each technique reveals different aspectsof the object and each has its own limitations. Forexample, X-ray radiography compresses an object’sthree-dimensional structural information into a two-

dimensional image (Figure 1(b)). CT provides depthinformation (Figure 1(b) inset), but requires expensive,stationary equipment, and special precautions to mini-mize radiation-exposure risk to personnel. Further-more, the narrow aperture of CT scanners prohibitsinvestigation of objects with large dimensions. Non-destructive ultrasonic testing can also be used, e.g.for cavity-presence evaluation (Gosálbez et al. 2006),but does not provide detailed three-dimensional struc-tural information. In non-destructive testing, arraymeasurements, i.e. measurements with multiple recei-ver points, are common (e.g. Hill and Dixon 2014;Ohara et al. 2017), but might suffer from the generationof waves (surface waves) that are undesired for high-resolution depth imaging of a material, as thesewaves lower the obtainable resolution.

In seismology, high-resolution three-dimensionalsubsurface images can be obtained using the active-source reflection method (Yilmaz 1999). The reflectionmethod uses surface sources and receivers and isapplied at scales from a few metres to hundreds ofkilometres. The method is graphically introduced inFigure 2. A source (the star) initiated at the surfacegives rise to seismic waves that propagate in the sub-surface. The waves are represented by the arrows

© The International Institute for Conservation of Historic and Artistic Works 2018

CONTACT Deyan Draganov d.s.draganov@tudelft.nl Department of Geoscience and Engineering, Delft University of Technology, Stevinweg 1, 2628CN Delft, Netherlands

STUDIES IN CONSERVATION, 2018https://doi.org/10.1080/00393630.2018.1437870

crossed by multiple arcs. Some of the waves (in black)reflect from in the subsurface at boundaries betweenstructures (e.g. layers) with different seismic properties(like seismic velocity and density) and are thenrecorded by surface receivers (the triangles). Therecording of the reflected waves is called reflectionresponse. The waves might reflect in the subsurfaceone or multiple times. The recording procedure atthe receivers is repeated for multiple active-sourcepositions, i.e. by moving the position of the star. Thereflection responses from all sources can be processedusing techniques from exploration seismology toproduce images of subsurface structures. In the caseof Figure 2, the image of the subsurface structureswill be the image of the subsurface layer.

To obtain a high-resolution image of the subsurfacestructures, the sources and receivers should be suffi-ciently many and sufficiently densely placed withrespect to each other. For small objects, like some art-works, a practical problem might arise. The size of the

Figure 1. (a) Painting on wood: Assumption of the Virgin (sixteenth century), private collection, Argentina. Photo: Tarea-IIPC. (b) X-ray photograph of the used mockup, which imitates painting on wood and consists of a wooden support, chalk-and-glue layer(beige), titanium-white-oil layer (white), and calcined-iron-oxide layer (brown). The inset shows a vertical slice of the mockup’sX-ray computed tomography image along the receiver line. The yellow rectangle indicates the part of the mockup we imagewith our method. (c) The mockup. The two shorter sides shown in the insets. Orange circles indicate wormholes, orange arrows– annual-growth rings.

receiverssource

surface

subsurfacelayer

Figure 2. Principle of seismic-reflection measurements. Asource (white star) at the surface is initiated and gives rise towaves (lines with arcs) propagating in the subsurface. Someof the waves reflect at subsurface boundaries, like the greylayer, and are recorded at the surface by receivers (triangles).Such waves are called reflected waves (black lines and arcs).Other waves propagate only along the surface and are calledsurface waves (grey lines and arcs).

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used sources might be such that receivers can beplaced only certain distances away from the sources,thus limiting the imaging resolution, especially of theshallow structures. In the test case we show below,the source and receivers have diameters of 5 mm.Thus, a receiver can be placed no closer than 5 mmfrom a source, thus limiting severely the resolution ofstructures that are shallower than 5 mm from thesurface.

Yet another practical problem can be the presenceof surface waves – energy propagating along anobject’s surface (illustrated in grey in Figure 2). Thesewaves provide no reflection information of the objectand are thus considered noise. The surface waves willlikely be the strongest arrivals at surface receiversmasking parts of the useful reflected waves and ham-pering successful imaging. Normally, surface wavesare suppressed by filtering (Yilmaz 1999). Such filteringis not a trivial task and quite often does not lead togood results, as it also damages the reflected wavesas well.

Because of the above-mentioned obstacles, wepropose an alternative application of the reflection-imaging method. We use transmission measurements,i.e. when receivers and active sources are placed ontwo parallel surfaces of an object to be investigated,for example, on the top and bottom of a painting onwood, see Figure 1(c). We transform the transmissionmeasurements into virtual reflection measurementswith virtual sources at the positions of the receiversusing the method of seismic interferometry (SI) withactive sources (Draganov et al. 2007; Wapenaar et al.2011).

Generally, SI is known as the process of retrievingthe seismic response (direct waves, surface waves,reflections, refractions) between two receivers fromthe cross-correlation of recordings at the two receiversfrom sources effectively surrounding these two recei-vers (e.g. Campillo and Paul 2003; Wapenaar andFokkema 2006; Wapenaar and Snider 2007; Brenguieret al. 2008). When the receivers are at the surface ofthe earth, for example, only sources in the subsurface

are required, for example, along a hemisphere thatfinishes with the earth’s surface. The latter principle isgraphically explained in Figure 3. Let us have a hom-ogenous subsurface with one reflecting object in it(grey). Sources in the subsurface are present alongthe complete thick dashed black line. The individualwaves (arrows) from sources (white stars) are recordedby the receivers (triangles). Let us cross-correlate therecorded wave arriving directly from a source to theleft receiver (direct arrival – dashed arrow) with thewave recorded at the right receiver after reflecting atthe surface and at the object inside the medium(reflected arrival – continuous arrows). The cross-corre-lation process effectively eliminates the common travelpath (dashed-arrow part). The cross-correlation processis repeated for all source (white-star) positions. Con-secutive summation of the separate correlations fromall the sources retrieves a reflection arrival at theright receiver from a virtual source (black star) at theposition of the left receiver.

When retrieval of specific events is of interest, e.g.reflected waves, on the bases of stationary-phase argu-ments, it can be shown that sources are required onlyinside the stationary-phase region (lower dashedellipse in Figure 3) for the event of interest (Snieder2004). The stationary-phase region is the regioninside which a function, in our case the correlationresults from the individual sources in Figure 3, showsvery little variation (i.e. is nearly stationary). Conse-quently, with sources close to and at the surfacewhere receivers are placed (upper dashed ellipse inFigure 3), mainly surface waves are retrieved. Withsources and receivers placed on opposing sides, i.e.using transmission measurements, mainly reflection

Figure 3. Principle of SI. Sources (white stars) are placed insidea homogenous medium along a boundary (thick dashed blackline), which finishes at the surface. Two receivers (triangles) areplaced at the surface. The medium contains only one reflectingobject (grey). Propagating waves are represented by thedashed and continuous arrows. The dashed ellipses indicatestationary-phase regions. After application of SI, the left recei-ver is turned into a virtual source (black star).

Figure 4. Explanation of wave types: (a) longitudinal (P-) wave– the particles (grey circles) vibrate in the direction of thepropagation of the wave; (b) and (c) transversal (S-) waves –the particles vibrate in a direction perpendicular to thedirection of the propagation of the wave. When the wave pro-pagates along the x-coordinate axis, an S-wave with particlevibration (b) along the z-coordinate axis is called SV-wave,while (c) along the y-coordinate axis – SH-wave.

ULTRASONIC IMAGING OF ARTWORKS WITH SEISMIC INTERFEROMETRY 3

arrivals are retrieved; surface waves would hardly beretrieved (Draganov et al. 2007). We use this latter prin-ciple for surface-wave suppression in our method.

Another advantage of using SI to turn transmissionmeasurements into reflection measurements withvirtual sources at the position of the receivers ishaving receivers very close to the retrieved virtualsource – 1 mm in the test case we show below.

SI by cross-correlation assumes medium withoutwave-energy loss during the wave propagation (Wape-naar and Fokkema 2006; Wapenaar et al. 2011) due tointrinsic processes like the internal friction of thematerial. However, ultrasonic waves propagatingthrough solid objects usually experience intrinsicenergy loss. Because of this, we use SI by multidimen-sional deconvolution or MDD (Wapenaar, Slob, andSnieder 2008; Wapenaar et al. 2011). This SI techniquecan be applied to media with energy loss due to intrin-sic processes and still retrieve reliable results.

In practice, the seismic-reflection method is mostcommonly applied with longitudinal waves (P-waves),i.e. waves for which the particle vibration is in the direc-tion of propagation of the wave (see Figure 4(a)).

To apply the method to artworks to image theirinternal structures, the wavelength used (i.e. thespatial period of the wave) should be shorter or com-parable to the size of an object’s internals. As the resol-ution increases with a decrease of the wavelength,sufficiently high frequencies should be used toachieve a high imaging resolution. For the test casebelow, we use ultrasonic frequencies although usinghigh frequencies alone might not solve the problem.The P-wave velocities inside artworks could result inwavelengths not providing the required resolution.With relatively higher P-wave velocities, like in metalor wood, the wavelengths might also be relativelylong. For the case of wood, for example, to seeannual-growth rings as separate structures, the wave-length should be shorter than four times the distancebetween neighbouring rings.

To obtain a higher spatial resolution, we make use ofreflected transverse waves (S-waves), because for thesame material, they are characterized by lower vel-ocities than the P-waves. This means that for a sourcesignal characterized by the same centre frequency,the S-wave would have a shorter wavelength thanthe P-waves as the former are characterized by alower velocity. The S-waves are waves for which theparticle vibration is in a direction perpendicular tothe direction of the propagation of the wave, seeFigure 4(b,c). If a wave propagates in a horizontal direc-tion, one can have S-waves whose particles vibrate (i.e.are polarized) in the vertical direction and thus com-monly labelled SV-waves, see Figure 4(b). An S-wavecould also be polarized in the second horizontal direc-tion. Such a wave is commonly labelled SH-wave, seeFigure 4(c). Both SV- and SH-waves are characterized

by the same velocity if a material is characterized bythe same properties in all spatial directions.

To record reflected SV-waves at the surface of anobject, transducers sensitive to particle vibration inthe vertical direction are used. Such transducers willalso sense P-waves, converted at an object’s internalstructure boundary from SV-waves. This means thatthe same reflector inside an object will give rise totwo recorded reflection arrivals. They are recorded atdifferent times, because the velocity of the two wavetypes is different. Applying imaging to such recordingscould lead to artificial (double) structures in the finalimages.

To avoid this, we use transducers sensitive to theparticle vibration in the horizontal direction sensingSH-waves. An advantage of using SH-waves is that ina 2D geometry, when the source line is verticallybelow the receiver line and forms one plane with it,the SH-waves decouple from the P- and SV-waves.This suppresses the recording of converted waves.Nevertheless, P- and converted waves might still berecorded due to 3D scattering.

Mockup and analysis

To demonstrate our method, we record ultrasonic dataon a mockup imitating a painting on a wooden support(Figure 1(c)). The base of the mockup is made of 100years old, 21 mm-thick poplar wood. The base iscovered with three layers: bottom – chalk and glue;middle – titanium white oil; top – calcined iron oxide.The mockup imposes high requirements on the resol-ution of the imaging methods to be used because ofthe mockup’s thinness, the very short distancebetween the wood’s annual-growth rings, and thesmall size of the possible damages inside the woodensupport. For conservation, it is important to know: con-dition of the wooden support (degradation positionand dimensions); and if and where the chalk-and-glue layer detaches from the wood. The shorter sidesof the mockup (insets in Figure 1(c)) reveal multiplewormholes and growth rings at the bare side (rightinset) and only growth rings at the side covered withall three layers (left inset).

As sources and receivers, we use Fuji Ceramics piezoceramic transducers with a diameter of 5 mm. To havegood contact with the material, and thus minimal lossof signal energy due to contact, we couple the transdu-cers to the mockup using an S-wave couplant. We placethe receivers along the Plexiglas®-covered measuringtape (Figure 1(c); the blue triangles in Figure 5(a)). Ina real painting on wood, the receivers would beplaced on the top iron-oxide layer, which is verysmooth and would provide good coupling. Themockup’s iron-oxide layer is rough and, thus, weplace the receivers on the smooth oil layer (top ofmockup). The impulsive source transducers (e.g. the

4 D. DRAGANOV ET AL.

blue star in Figure 5(a)) are placed on the opposite side(bottom) of the mockup vertically below (accuracy of0.5 mm) the receivers. The transducers are sensitiveto SH-waves, i.e. particle vibration as in Figure 4(c).The thickness of the mockup between the sourcesand the receivers is 23 mm.

For real artworks, possible damage due to using theS-wave couplant to attach the transducers should beavoided. This could be achieved if the investigationarea is covered with gel film based on methylcellulose(Doherty et al. 2011). Another possibility might be theutilization of non-contacting laser ultrasonic equip-ment, using lasers as both sources and receivers (e.g.Nishizawa et al. 1997; Draganov et al. 2007; Blumet al. 2010). Note that when using a laser source, theintensity must be sufficiently low to avoid damage tothe objects. Yet another possibility might be the utiliz-ation of air-coupled transducers. In this case, though,only P-waves will be recorded, as S-waves do not

propagate in air (fluids in general). This would meanthe recording of converted S-to-P-waves, but also P-waves propagating inside the mockup. The presenceof such waves would make the interpretation of thefinal image difficult.

To record ultrasonic waves, we use a solid constructof a thin polyvinylchloride plate with eight receiversfixed in it every 6 mm (Figure 1(c)). The receiversform one line. We perform the measurements asfollows. We attach a source to the bottom of themockup vertically below the receiver line’s beginning,initiate the source, and record the transmissionresponse along the array. To increase the ratio of theuseful signal over the background non-repeatable elec-tronic noise and vibration, the same measurement isrepeated 128 times. The individual 128 recordings ateach receiver are summed to obtain final recordingsat eight receivers from this source position. The solid-construct array is then moved along the receiver line

Figure 5. (a) Illustrative representation of set-up. A sine signal from function generator is amplified and fed to a source transducer(star). Transmissions detected by receiver transducers (triangles) go to an oscilloscope. The transducers are sketched on the slicefrom the inset in Figure 1(b). Coloured arrows illustrate travel paths of three arrivals (see main text). (b) and (c) Transmissioncommon-source gathers for a source at the mockup’s bottom at (76,23) mm and at (99,23) mm, respectively. For visualization,panels are clipped and the images in (b) and (c) are linearly interpolated to include an extra point between receivers. Before clip-ping, the recording at each receiver is normalized (see text).

ULTRASONIC IMAGING OF ARTWORKS WITH SEISMIC INTERFEROMETRY 5

by 1 mm and a new recording from the same source istaken. The moving and recording are repeated fivetimes. This produces transmission recordings at 48receiver positions. We call the collection of theserecordings a transmission common-source gather(CSG). After obtaining a complete transmission CSG,we move the source by 1 mm towards the receiverline’s end and repeat the measurements. In total, weuse 45 source positions resulting in 45 transmissionCSGs.

Each source initiates an impulsive sine-wave signalwith a centre frequency of 1 MHz. The signal is pro-duced by an Agilent 33210A function generator, andis afterwards amplified by an ENI 2100 RF amplifierbefore being fed to the source (Figure 5(a)). The trans-mission responses are recorded on a YokogawaDL9240 oscilloscope (Figure 5(a)) using a samplingrate of 20 ns.

Figure 5(b,c) shows example transmission CSGs forsources at horizontal positions 76 and 99 mm, respect-ively. In both transmission panels, the earliest, andclearest, curved arrival is the direct transmitted SH-wave. The blue arrow in Figure 5(a) sketches a pathof such an arrival. The direct transmitted SH-wave is fol-lowed by reverberations: some represent internal scat-tering at structural contrasts inside the mockup (themagenta arrow in Figure 5(a)); others represent reflec-tions from the contrasts after the direct SH-wave hasreflected at the top of the mockup (the cyan arrow inFigure 5(a)). The ringing horizontal arrivals earlierthan the direct SH-wave are electromagnetic noisedue to induction of the source signal to the receivercables. Although this noise is weak, in the figure itappears relatively strong due to the signal amplifica-tion applied for visualization – at each receiver, therecorded transmission is amplified by normalizing theamplitude at each time sample with the root meanenergy inside a running window of 0.01 ms centredat that time sample.

The transmission CSGs in Figure 5(b,c) are shown intravel time of the waves from the source to the recei-vers. This time can be transformed to travel-path dis-tances if one knows the propagation velocities insidethe object. Alternatively, one can estimate theaverage SH-wave velocity through the mockup usingthe thickness of 23 mm and the travel time of thedirect SH-wave between a vertical source–receiverpair. As this velocity is useful, we estimate it by extract-ing the recording from each vertical source–receiverpair, summing these recordings to improve thesignal-to-noise ratio, picking the time of the firstarrival – the direct SH-wave, and dividing themockup’s thickness by the picked time. In this way,we estimate an average velocity of 1520 m/s. Thewavelength for this velocity is 1.52 mm, theoreticallyallowing imaging/interpretation of structures separ-ated by 0.5 mm. This theoretical value stems from the

requirement to have two consecutive reflection arrivalsin a recording separated by at least quarter of a wave-length (Yilmaz 1999). We take here a third as a safercriterion.

The initiated signals’ centre frequency of 1 MHz isnot necessarily the centre frequency of the recordedsignals. Figure 6(a,b) shows the amplitude spectra ofthe CSGs from Figure 5(b,c), respectively: the mainenergy of the recorded signals peaks between 800and 900 kHz and quickly weakens away from the recei-vers closest vertically above the source. The lower peakfrequency and the loss of energy away from the sourceevidence intrinsic energy loss.

Reflection imaging of the mockup: amodelling example

We perform numerical-modelling tests to show whatcould be obtained using the reflection-imagingmethod in general. We simulate reflection measure-ments using a two-dimensional finite-difference mod-elling code (Thorbecke and Draganov 2011). Wecreate a numerical density model (Figure 7(a)) of themockup between the source and receiver lines seeninside the yellow rectangle in Figure 5(a). The coloursindicate the density values inside layers (representingthickness between annual rings) and scatterers (e.g.wormholes): white – density of 10 kg/m3; light grey –650 kg/m3; medium grey – 850 kg/m3; dark grey –1000 kg/m3; and black – 1050 kg/m3. We keep the vel-ocity constant at 1520 m/s, which is the estimatedaverage velocity of the SH-waves.

To show a best-possible imaging scenario, we donot model surface waves. As explained above, thesewaves are considered noise. Furthermore, we do notmodel the top of the mockup as a free boundary. Inthe case for the laboratory measurements, due to theair above the mockup, the top of the mockup is afree boundary. Having a free boundary will totallyreflect a wave incident at that boundary back insidethe object resulting in recording reverberations (free-surface multiple reflections) between the seismic-prop-erty contrasts inside the mockup and the top of themockup. Recorded free-surface multiples lead to artifi-cial structures in the obtained image. Specially devel-oped processing techniques aim at eliminating free-surface multiples from data. By not modelling a freeboundary, we do not need to apply such techniques.

We further increase the resolution of the imaging,especially of deeper structures, by not modellingenergy loss due to intrinsic processes.

We model receiver responses at the actual receiverpositions. We simulate reflection measurements byplacing a source at each receiver position. We use animpulsive source signal characterized by a Rickerwavelet (Ricker 1953) with a centre frequency of1 MHz. Figure 7(c–e) shows simulated reflection CSGs

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for a source (the star) at 53, 70, and 90 mm, respect-ively. The vertical axis is expressed in the time wavespropagate from a source to the receivers – reflectedwaves’ two-way travel time. We indicate the reflectionfrom the bottom of the first layer (R1), from the bottomof the mockup (R2), from scatterer 1 (Sc1), and fromscatterer 3 (Sc3).

To obtain a depth image (Figure 7(b)) of the numeri-cal model, we apply to the simulated reflection CSGsfrom all source positions prestack depth migration(Thorbecke, Wapenaar, and Swinnen 2004). Migrationis an algorithm that uses a velocity model to collapsethe reflection arrivals to their corresponding reflectionpoints inside objects (Yilmaz 1999), in our case insidethe mockup. We use a homogeneous velocity modelof 1520 m/s. We see that the different layer boundariesare imaged at their exact places. Close to the receiver-line ends, the amplitudes of the imaged boundaries arelower because there less reflection CSGs contribute tothe final image. The top and bottom of the five scat-terers are delineated by a vertical pair of eventscurved to a different degree (e.g. the black pointersin Figure 7(b)). The dominant wavelength of the mod-elled waves is 1.52 mm. This wavelength is comparablewith the diameter of between 1 and 2 mm of the visiblewormholes in the mockup, meaning the wormholeswill be imaged as reflecting objects with limited dimen-sions. Howmuch of the top and bottom of a scatterer isimaged depends on the illumination of that scatterer.The illumination, in turn, depends on the source–recei-ver positions and on the layering inside the mockup.For example, Sc1 and Sc4 are imaged at their topright parts clearly, which indicates that these two

scatterers are being illuminated mainly from theright. The bottom left part of Sc4 is partly interpretable,but that is hardly possible for Sc1, showing that thereceivers recorded very little reflected energy fromthe bottom of Sc1. For the other three scatterers, theillumination of the top left and right parts is morebalanced; for Sc3 and Sc5, also the bottom parts areinterpretable.

After showing the quality of the reflection imagethat could be obtained with the idealized numericalmodel and acquisition above, we introduce themethod we want to use and show the results weobtain from the laboratory data of the mockup.

Method

In the appendix, we explain the theory of the methodwe use. There, we introduce the symbols that we alsouse in this section.

Figure 5(b,c) shows the transmission CSGs, what wealso call transmission response Tv(xB, xi , t) in theappendix, smeared by the source time function (STF),i.e. the length in time of the source signal, observedat the 48 receiver positions (xB from (53,0) to (100,0)mm) from a source xi at positions (76,23) and (99,23)mm, respectively; t indicates time; and v in the super-script – that particle velocity was recorded. Using thetransmission responses, we can retrieve the reflectionresponse Rv with SI by cross-correlation as explainedin the Introduction; see the appendix for a mathemat-ical explanation. Even though we feed a sine wavelet tothe sources, the STFs are elongated in time because weuse unshielded transducers causing reverberations of

Figure 6. Amplitude frequency spectrum of the transmission common-source gather shown (a) in Figure 3(b) and (b) in Figure 3(c).

ULTRASONIC IMAGING OF ARTWORKS WITH SEISMIC INTERFEROMETRY 7

the sine wave inside the transducers themselves.Having long STFs would result in lower-resolutionimages – the reflecting boundaries will appear thickerin the image. Ideally, knowing (measuring) a source’sSTF allows removing it using a process known aswavelet deconvolution. But measuring individual STFsat ultrasonic scales is difficult, and only estimates thatapproximate the true STFs could be obtained. Usingthe estimates instead of the true STFs might againlower the resolution. Because of this, we choose toretrieve the reflection response using other SImethods – by cross-coherence and MDD, as thesetwo methods eliminate the STFs (see the appendix).

We first apply SI by cross-coherence (relation A3 inthe appendix). As the transmission recordings sufferfrom energy loss due to intrinsic processes, thelater reflections retrieved using cross-coherencewould be unrealistically weak relative to the earlierreflections. Furthermore, next to the retrieved phys-ical reflections, also non-physical reflections wouldbe retrieved (Draganov et al. 2010; Draganov, Heller,and Ghose 2012; King and Curtis 2012). Non-physicalreflections are retrieved events that cannot berecorded using a physical source at the position ofthe virtual source. Non-physical events are undesired,

as they deteriorate the imaging quality. Attemptingto increase the amplitude of possible retrieved laterreflections, we amplify the recorded transmissionCSG, effectively trying to compensate for the intrinsicenergy loss. The best amplification depends on anobject’s energy attenuation. Not having an estimateof the attenuation, we test amplifying the data bymultiplying the signal’s amplitude at each timesample by t, t2, and t3. For our dataset, the bestresults appear to be the ones using t3.

Figure 8(a) shows the retrieved Rv , or as explained inthe appendix – the cross-coherence function Cch,using the amplified transmission CSGs Tv(xB, xi , t)(Figure 5(b,c)). The virtual source is at xB = (75,0) mm,the receivers – at multiple positions xA = (53,0) toxA = (100,0) mm. As relation (A3) predicts, both posi-tive and negative times are retrieved in Figure 8(a). Ifthe source array were sufficiently long, the retrievedreflection response at positive and negative timeswould have been the same, and we could have takenthe positive times to obtain the complete retrievedreflection response. For a horizontally layeredmockup, sufficiently long would mean extending thesource array on each side of the receiver array bymore than half the length of the receiver array.

Figure 7. (a) Numerical model of the density inside the yellow rectangle in Figure 3(a). Five scatterers are marked by crosses/numbers. White colour stands for a density of 10 kg/m3, light grey – 650 kg/m3, medium grey – 850 kg/m3, dark grey –1000 kg/m3, and black – 1050 kg/m3. (b) Image of the mockup’s model obtained from migrating the simulated reflection measure-ments. Pointers indicate vertical pairs of events characteristic of the scatterer. (c)–(e) Simulated reflection common-source gathersfor sources (stars) at (53,0) mm, (70,0) mm, and (90,0) mm, respectively. The reflection from the first layer’s bottom is labelled R1,from the model’s bottom – R2, from scatterers 1 and 3 – Sc1 and Sc3, respectively.

8 D. DRAGANOV ET AL.

For our source–receiver geometry and the complexinternal structure of the mockup, due to stationary-phase considerations (Snieder 2004), some parts of Rv

would be better retrieved at positive times, otherparts – at negative times. As the mockup is stronglyheterogeneous, using only the source–receiver geome-try it is not easy to decide, like for a horizontally layeredmockup, which times should be selected. Because ofthis, we compare visually the quality of the retrievedpositive and negative times. From the comparison,we decide for virtual-source positions fromxB = (67,0) to xB = (86,0) mm to select the positive

times and discard the negative times (Figure 8(b)).For virtual-source positions from xB = (53,0) toxB = (67,0) mm, we take the time-reversed negativetimes for receivers to the right of the virtual sourceand concatenate them to the positive times taken forreceivers to the left of the virtual-source position(Figure 8(c)). For virtual-source positions fromxB = (86,0) to xB = (10,0) mm, we do the opposite(Figure 8(d)).

In an active-source experiment with pure SH-waves,nothing would propagate faster inside the mockupthan the direct SH-wave and possibly a refracted

Figure 8. (a) Result from SI by cross-coherence for a virtual source at xB = (75,0) mm obtained from amplified transmissions. (b)–(d)Illustration of which parts of the retrieved positive and negative times are used for a virtual source at xB = (75,0) mm, xB = (60,0)mm, and xB = (90,0) mm, respectively. See main text for details. For visualization, the images are interpolated as in Figure 3(b,c).

ULTRASONIC IMAGING OF ARTWORKS WITH SEISMIC INTERFEROMETRY 9

wave at longer offsets. This means that in the retrievedvirtual CSGs events earlier than the expected direct SH-wave would be artificial, except for possible retrievedrefractions. Because of this, we set to zero everythingearlier than the expected direct SH-wave. Note thatfor reflection imaging, the refracted arrivals are unde-sired and can also be set to zero.

Figure 9(a) shows the final retrieved reflection CSGfor a virtual source at xB = (75,0) mm. The pointersindicate possible retrieved reflections from theseismic-property contrasts inside the mockup. Com-parison with the numerically modelled responseshows that these events might indeed be retrievedreflections. We also see that the retrieved events areinterpretable only at earlier times, but even at thesetimes not interpretable along the complete receiverline. The partial retrieval of reflection events alongthe line might be due to less-than-optimal illuminationfrom the active sources. Note that because of theenergy attenuation, some of these events might actu-ally be retrieved non-physical reflections.

We now apply SI by MDD using Equations (A7) and(A8) for Gtyz

cch. The latter is a multidimensional factor esti-mated from the measured data that tries to correct theless-then-optimal result Cch for its shortcomings.To perform the inversion in Equation (A7), we need toestimate G

tyzcch and Cch. We estimate them from SI by

cross-coherence (Equation (A3)), but without applyingtime-dependent amplification to the transmissionCSGs. Figure 10(a) shows the result for a virtual sourceat (75,0) mm. The result is dominated by eventspassing through the virtual-source position at time 0 s.These events are obtained from the cross-coherenceof arrivals that would be recorded by the receivers inthe absence of a free boundary at the top of themockup. Keeping only the retrieved arrivals passingthrough the virtual-source position at time 0 s and thearrivals around them as in the example in Figure 10(b)(see Wapenaar et al. [2011] for details on why keepingonly these arrivals), we obtain an approximation Gv

cch

for measurements of the particle velocity v instead ofGtyzcch for measurements of the shearing stress tyz . Isolat-

ing the result in Figure 10(b) from the complete result,Figure 10(a) gives an approximation of Cch (Figure 10(c)) as required for the inversion of Equation (A7).

To estimate Gtyzcch from Gv

cch, we use the following. Inthe absence of a free surface at the level of the recei-vers, the wavefields recorded at the receivers continuetravelling away from them. In such a case, a shearing-stress recording (tyz) at the receivers can be shown tobe proportional to vy . This relation can be obtainedusing the elastic equivalent of the acoustic equationof motion. When the seismic parameters just belowthe receivers do not change (like in our case of achalk-and-glue layer), the proportionality factor is oneover the cosine of the angle between the propagationdirection of the first arrival at the virtual-source position

with respect to the receiver surface. We approximatethis angle by the angle between the vertical and theline connecting the virtual- and active-source positions.We further assume that particle-velocity recording inthe absence of a free surface at the receivers can beobtained from the particle-velocity recording in thepresence of a free surface by windowing.

Results and discussion

We retrieve reflection CSGs using SI by cross-coherenceand by MDD for virtual sources at all receiver positions.We then apply band-pass filter between 0.4 and1.2 MHz (Figure 9(a,b)). The cross-coherence resultexhibits interpretable possible retrieved reflectionsuntil about 0.01 ms (the pointers in Figure 9(a)), whilein the MDD result the later possible retrieved reflec-tions are more interpretable (the pointers in Figure 9(b)). The reason for this might be that SI by MDDtakes the wave-energy loss due to intrinsic processesinto account and/or that it (partly) compensates forpossible illumination inhomogeneity. On the otherhand, the less-than-optimal estimation of Gtyz

cch mightbe the reason for not seeing earlier events in the SI-by-MDD result.

After retrieving all reflection responses, we applyprestack depth migration (Thorbecke, Wapenaar, andSwinnen 2004) to obtain a depth image of themockup under the receiver line. For the migration,we use a homogeneous velocity of 1520 m/s as esti-mated from the transmission measurements asdescribed above. Figure 11(a,b) shows the depthimages of the mockup obtained from the MDD andcross-coherence results, respectively. After migration,we apply an extra high-cut filter at 1 MHz to improveinterpretability. For comparison, in Figure 11(c) weshow the part of the X-ray CT image of the mockupinside the yellow rectangle in Figure 5(a).

The SI images in Figure 11 exhibit inclined linearevents, starting at the left and right sides anddipping to the centre, not present in the CT image.These are artificial events because of the limited aper-ture, due to both SI and imaging, which could be sup-pressed by using longer acquisition geometry. The CTimage (Figure 11(c)) shows that the chalk-and-gluelayer is thick between 2 and 1 mm at horizontal dis-tance 53 and 100 mm, respectively. In both SI images,the bottom of the chalk-and-glue layer is partlyimaged at such depths.

Inside the wooden support, the SI-by-MDD image(Figure 11(a)) reveals in general a superior picture thanthe SI-by-cross-coherence image (Figure 11(b)). The SI-by-MDD image is less noisy and more continuous inthe lateral direction. This allows for an easier interpret-ation of the wooden support’s structure, with the mostprominent feature being the dome-like feature ofseveral layers with an apex around (85,5) mm. This

10 D. DRAGANOV ET AL.

feature and a few other clearly interpretable seismic-property contrasts in the SI-by-MDD image are theannual-growth rings imaged in the CT image as well.

The CT image reveals five scatterers, marked by theorange crosses in Figure 11(c). Scatterers Sc1 to Sc4 arewormholes. The nature of Sc5 is unclear, but it might bea density contrast. As explained in the modellingexample, the presence of the scatterers would be evi-denced by vertical pairs of curved events. In the SI-by-MDD image, Sc3 and Sc5 are indicated by the pres-ence of the lower part of the curved pair of events, andcould be interpreted as scatterers. In the SI-by-cross-coherence image, the vertical pair is present for Sc5.The absence of the upper event for Sc5 in the SI-by-MDD image might be coming from the less-than-optimal estimation of G

tyzcch. Even though parts of

some of the scatterers in the SI images could be inter-preted, the signal-to-noise ratio of the pair of curvedevents is low, which makes the interpretation of thescatterers difficult. The signal-to-noise ratio, and thusinterpretability, could be increased if 2D acquisitiongeometry of source and receiver transducers is used.For example, this might mean using several lines ofsource and of receiver transducers instead of thesingle line of source and single line of receiver transdu-cers we use. Using 2D acquisition would also allowobtaining a 3D image of the mockup from 3Dmigration. This will further remove possible ambiguityin a 2D image that might arise from the migration ofreflection or scattering events not inside the plane ofthe source and receiver lines we use. When using 2Dacquisition, to avoid the appearance of strong con-verted and P-waves, care should be taken to recordthe transmission response from a source transduceronly at receiver lines that are close to lying verticallyabove that source transducer.

To compare the resolution of the SI images to thatfrom the CT scan, we overlay the latter with each ofthe SI images (Figure 12(a,b)). The overlays show thatSI by MDD has imaged the annual-growth rings atthe same depth as the CT image. The resolution ofthe two images is also comparable. Where the CTimage shows strong annual-growth ring contrasts,the SI-by-MDD image shows them as well. In Figure12(c), we overlay the CT scan with an image obtainedfrom the summation of the SI-by-cross-coherence andSI-by-MDD images. We can see that taken complemen-tary, the two SI images provide a nearly completeimage of the chalk-and-glue layer.

We compare our results to a CT image, but obtaininga CT image requires expensive, stationary equipmentand special precautions. The application of CT is alsolimited by the aperture of the CT scanner. Ourmethod can be used with off-the-shelf mobile equip-ment and can be applied even to large artworks forimaging of areas of interest. On the other hand, a CTimage can be obtained of objects with any roughnessof the surfaces. Rough surfaces might cause poor trans-ducer/object contact thus limiting the utilization ofultrasonic measurements.

The validation of our results with the CT imageshows that our method can provide high-resolutioninformation of the material structure and condition ofartworks and thus be a valuable new tool for non-inva-sive depth characterization for conservation and restor-ation purposes.

Conclusions

We proposed a new non-invasive ultrasonic method forhigh-resolution depth imaging of artworks. Themethod uses transmission measurements of transverse

Figure 9. Reflection response (a) retrieved using SI by cross-coherence, (b) retrieved using SI by multidimensional deconvolution,and (c) simulated using the numerical modelling for a (virtual-)source co-located with the middle receiver. For visualization, thepanels are clipped; the images in (a) and (b) are interpolated as in Figure 3(b,c). The pointers indicate possible retrieved reflections.

ULTRASONIC IMAGING OF ARTWORKS WITH SEISMIC INTERFEROMETRY 11

Figure 10. (a) Result retrieved using SI by cross-coherence without amplifying the transmissions for a virtual source at xB = (75,0)mm. (b) Selecting the dominant arrivals from (a) that pass through the virtual-source position at time 0 s. (c). Result from the iso-lation of the events in (b) from the panel in (a). For visualization, the images are interpolated as in Figure 3(b,c).

Figure 11. Depth image after migrating the reflectionsretrieved using SI by (a) multidimensional deconvolution and(b) cross-coherence. (c) Image from X-ray computed tomogra-phy. Scatterers (e.g. wormholes) in the computed-tomographyimage indicated by orange crosses and numbered from 1 to5. Example annual-growth rings indicated by pointers.

Figure 12. Overlay of the images from (a) Figure 9(a,c) and (b)Figure 9(b,c). In (c) the result of the summation of the imagesfrom Figure 9(a,b) is overlaid on the image from Figure 9(c). Fora better contrast, the grey scale from Figure 9 is exchanged forblack and white.

12 D. DRAGANOV ET AL.

waves. The shorter wavelength of the transverse waves,compared to longitudinal waves for the same frequen-cies, contributes to the higher spatial resolution. Ourmethod makes use of SI by multidimensional deconvo-lution to turn the transmission measurements intoreflection measurements from virtual sources at thereceiver position. Retrieving reflections from trans-missions suppresses retrieval of surface waves, whichnormally are present in actual reflection data and inter-fere with it. Application of SI by multidimensionaldeconvolution also results in the compaction of thesource wavelet and thus increases the resolution ofthe final ultrasonic image. Having obtained reflectionmeasurements allows application of advanced seismicimaging techniques as used in the seismic-explorationindustry. We applied our method to a mockup of anantique painting consisting of a 21 mm-thick woodensupport of about 100-year-old poplar wood, a bottomlayer of chalk and glue, a middle layer of titaniumwhite oil, and a top layer of calcined iron oxide. We per-formed transmission measurements with receivers onthe titanium-white-oil layer and sources verticallybelow them on the opposite side of the mockup.From the measured transmission data, we retrievedvirtual reflections, to which we consecutively appliedprestack depth migration to obtain a depth image ofthe mockup. The ultrasonic image revealed the baseof the chalk-and-glue layer, and inside the woodensupport – annual-growth rings and scatterers, likewormholes. Comparing our results to an image fromX-ray computed tomography, we confirmed that ourmethod has imaged the structures inside the mockupat the same depth and with resolution comparable tothat of the computed-tomography image. The vali-dation shows that our method can provide high-resol-ution information of the material structure andcondition of artworks and can be a valuable new toolfor non-invasive characterization in depth.

Acknowledgements

We thank two anonymous reviewers for their comments thathelped improve the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This research is supported by the Division for Earth and LifeSciences (ALW) with financial aid from the NetherlandsOrganization for Scientific Research (NWO) [grant numberVIDI 864.11.009].

ORCID

Deyan Draganov http://orcid.org/0000-0001-8606-1178

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Appendix

We introduce the basics of reflection retrieval from trans-missions using SI by cross-correlation, cross-coherence, andMDD.

Let Rv (xA, xB, t) denote the impulse reflection response ata receiver at xA from an impulsive source at xB, the superscriptv indicating that particle velocity is recorded, and x = (x, y, z),where axis x is oriented along the receiver line on themockup, y – across the line, and z – in the vertical direction.Tv (xA, xi , t) and Tv(xB, xi , t) denote transmission responsesmeasured at receivers at xA and xB, respectively, from animpulsive source at xi . The reflection and the transmissionresponses are related (Wapenaar and Fokkema 2006) through

{Rv(xA, xB, t)+ Rv(xA , xB, − t)}∗Sav (t)/

∑i

{Tv(xB, xi , − t)∗Tv(xA, xi , t)∗s(xi , − t)∗s(xi , t)}

(A1)

where s(xi , t) is the source time function (STF) of the source atxi and Sav(t) is the average of the autocorrelated STFs. Theasterisk denotes convolution, but convolution betweentime-advanced and time-retarded signals is equal to corre-lation. The above relation is SI by cross-correlation andshows how to retrieve the reflection response at xA due toa virtual source at xB. Equation (A1) assumes a medium

without energy attenuation caused by intrinsic processes,source boundary in the far field of the receivers, smoothlyvarying medium parameters across the boundary, andincludes a high-frequency approximation.

In the frequency domain, the convolutions of Equation(A1) become multiplications:

{Rv(xA, xB, v)+ (Rv(xA , xB, v))∗}Sav (v)

/∑i

{(Tv(xB, xi , v))∗Tv(xA, xi , v)(s(xi , v))

∗s(xi , v)}

(A2)

where the asterisk in a superscript indicates complex conju-gation, and v denotes angular frequency. If the right-handside (RHS) is divided by the amplitude spectrum of the trans-mission measurements at xA and xB, the denominator willcontain the square of the STF’s amplitude spectrum. The mul-tiplication of the STF with its complex conjugate in the RHS isalso equal to the square of the STF’s amplitude spectrum.Thus, applying SI by cross-correlation to the transmissionmeasurements normalized by their amplitude spectrum, weobtain SI by cross-coherence (Nakata et al. 2011):

Rv(xA , xB, v)+ (Rv(xA, xB, v))∗

/∑i

(Tv(xB, xi , v))∗Tv(xA, xi , v)

|T (xB, xi , v)v||Tv(xA, xi , v)|{ } (A3)

where | | denotes amplitude spectrum. As can be seen, theadvantage is that the STFs are completely removed. The dis-advantage is that for xA = xB, in the numerator in the RHS ofEquation (A3) one obtains the square of the amplitude spec-trum of the measured transmission response, which is sub-sequently removed by division with itself; this divisioneliminating completely the reflection information (clampedboundary condition; Vasconcelos and Snieder 2008).

As SI by cross-coherence is derived from SI by cross-corre-lation, it inherits the same assumptions.

SI by cross-correlation and cross-coherence aim to retrievethe impulse reflection response. This can be achieved whenthere is no energy attenuation in the medium and whenthe sources illuminated the receivers homogeneously fromall directions. In field or laboratory measurements, such situ-ations would be very difficult to achieve. Because of this, it isbetter to say that instead of Rv(xA , xB, v) the correlationCcr(xA, xB, v) or coherence function Cch(xA , xB, v) isretrieved. Wapenaar et al. (2011) showed that Ccr(xA, xkB, v)is connected to the actual impulse reflection responseRv(xA, x

jC , v) through

Ccr(xA, xkB, v) =∑j

Rv(xA, xjC , v)G

p(xkB, xjC , v) (A4)

where k indicates multiple virtual-source positions, subscriptC indicates a virtual-source position for the response Gp, pindicates measurements of acoustic pressure, and j is thenumber of receivers (virtual sources). As we use an elasticmedium with SH-waves, instead of the acoustic pressure,we actually measure the shearing stress tyz of the tractionvector tz acting across a plane normal to the vertical axisz. So, we exchange p for tyz . The matrix

Ccr(xA, xkB,v)=∑i

{(�Tv(xkB, xi , v))

∗Tv(xA, xi ,v)(s(xi ,v))

∗s(xi ,v)}

(A5)

is identical, except for the bar above T , to the RHS of Equation(A2). The bar indicates a measurement in a medium charac-terized by a homogeneous half space above the receivers

14 D. DRAGANOV ET AL.

(instead of having free surface). The matrix

Gtyz (xkB, xjC ,v)

=∑i

{(�Ttyz (xkB, xi ,v))

∗�Ttyz (xjC , xi ,v)(s(xi ,v))

∗s(xi , v)}

(A6)

practically shows how far the correlation function Ccr isfrom Rv . As both Ccr and Gtyz can be estimated frommeasured data, Equation (A4) can be solved for Rv bymatrix inversion. This process is known as SI by MDD. In

our case, we use stabilized least-squares inversion (e.g.Wapenaar et al. 2011).

Equation (A4) is written for cross-correlation, but can simi-larly be written for cross-coherence:

Cch(xA , xkB, v) =∑j

Rv(xA, xjC , v)G

tyzcch(x

kB, x

jC , v) (A7)

withGtyzcch(x

kB, x

jC , v) =

∑i

(�Ttyz (xkB, xi , v))

∗�Ttyz (xjC , xi , v)

|�Ttyz (xkB, xi , v)||�Ttyz (xjC , xi , v)|

{ }(A8)

ULTRASONIC IMAGING OF ARTWORKS WITH SEISMIC INTERFEROMETRY 15