Data-Driven Imaging in Anisotropic Media

Transcription

1 18 th World Conference on Non destructive Testing, 16- April 1, Durban, South Africa Data-Driven Iaging in Anisotropic Media Arno VOLKER 1 and Alan HUNTER 1 TNO Stieltjesweg 1, 6 AD, Delft, The Netherlands Phone: +31 () , e-ail: arno.volker@tno.nl Abstract. Anisotropic aterials are being used increasingly in high perforance industrial applications, particularly in the aeronautical and nuclear industries. Soe iportant exaples of these aterials are coposites, single-crystal and heavy-grained etals. Ultrasonic array iaging in these aterials requires exact knowledge of the anisotropic aterial properties. Without this inforation, the iages can be adversely affected, causing a reduction in defect detection and characterization perforance. The iaging operation can be forulated in two consecutive and reciprocal focusing steps, i.e., focusing the sources and then focusing the receivers. Applying just one of these focusing steps yields an interesting interediate doain. The resulting coon focus point gather (CFP-gather) can be interpreted to deterine the propagation operator. After focusing the sources, the observed travel-tie in the CFP-gather describes the propagation fro the focus point to the receivers. If the correct propagation operator is used, the easured travelties should be the sae as the tie-reversed focusing operator due to reciprocity. This akes it possible to iteratively update the focusing operator using the data only and allows the aterial to be iaged without explicit knowledge of the anisotropic aterial paraeters. Furtherore, the deterined propagation operator can also be used to invert for the anisotropic ediu paraeters. This paper details the proposed technique and deonstrates its use on siulated array data fro a specien of Inconel single-crystal alloy coonly used in the aeronautical and nuclear industries. Keywords: Ultrasonic, iaging, focusing, phase array, anisotropic. 1. Introduction Phased array iaging is becoing an increasingly powerful tool for characterizing the interiors of objects. Additionally phased array systes are becoing ore coon in use. To construct a high quality iage, detailed inforation about the actual velocity field in a ediu is required. Using an incorrect velocity yields a blurred iage and ay produce significant artifacts, which can lead to erroneous interpretation. This is particularly the case in anisotropic edia. Anisotropic aterials are being used increasingly in high perforance industrial applications, particularly in the aeronautical and nuclear industries. Soe iportant exaples of these aterials are coposites, single-crystal and heavy-grained etals. In this paper we introduce a generalized concept that allows the extraction of the iaging operators directly fro the data, without the need to ake any prior assuptions about the ediu. We deonstrate the concept based on odeled finite difference data using a strongly anisotropic single crystal steel.. Coon focal point ethod The forward odeling procedure is conceptually explained in Figure 1, using a wave field S( z ) operator forulation [1]. In Figure 1, is the eitted wave field fro a wedge transducer at the steel-wedge interface. This operator includes elastic transission effects fro the wedge ( z ) into the steel. The wave field propagation operator W +, z, extrapolates the wave field fro the top surface to the back wall. Note that z ay vary with the lateral coordinate.

2 ( z ) The wave field is reflected fro the back wall, where R + W ( z, z ) reflection fro the backwall. The upward propagation operator describes the angle dependent propagates the waves to the outer surface at z, again z ay vary laterally. Part of the wave field is detected D( z ) by a wedge transducer, described by and another part is reflected back, described by R ( z ). Each pass through the feedback loop yields another, higher order skip. The wave field description is in the teporal frequency doain. z z ( x) The inversion odel is paraeterized with = z z ( x) and =, where x is the lateral coordinate. The data atrix for priary reflections, i.e., ignoring ultiple reflections can be written as: P + + ( z ) D( z ) W ( z, z ) R ( z ) W ( z z ) S( z ) =. ( 1), Figure 1 Scheatic illustration of that described wave propagation in elastic, anisotropic edia, The wave field is being generated by an arbitrary source array (S) that both describes the directivity and the signature. The wave field propagates down (W + ), gets reflected (R + ), where the reflection operator describes general angle dependent reflectivity. The second propagation (W - ) is back to the surface and the detector response is expressed by D. Multiple reflections are generated by the feedback loop. Iaging can be forulated in ters of two consecutive focusing steps [,3], focusing the sources and then focusing the receivers. The focusing operator for the sources is defined as: and for the receivers: ( z, z ) S( z ) F( z z ) = δ ( z ) + W, j, ( ) F T i T ( z, z ) ( z ) ( z, z ) = δ ( z ) D. ( 3) W The bold sybols indicate atrices, while the noral font with a subscript indicates a vector. δ ( ) The vector j z indicates a band liited delta function, with essentially one non-zero eleent at location j. These focusing operators are actually vectors, where the sybol T indicates that the vector is a row vector. Applying this to the data atrix yields: F T i T + ( z, z ) P( z ) Fj( z, z ) = Fi ( z, z ) D( z ) W ( z, z ) R( z ) W ( z, z) S( z ) Fj( z, z ) = R ( z ) ij i. ( 4)

3 This procedure extracts one eleent fro the reflection atrix. Norally confocal iaging is used, i.e., i = j. If just one focusing step is applied, an interesting interediate doain is obtained. The result is called the coon focus point gather (CFP): P j ( z z ) P ( z ) F ( z, z ) = D( z ) W ( z, z ) R( z ) δ ( z ), j =. ( ) The travel tie of the coon focus point response is fro the target point to the receiver positions at the surface. While the focusing operator contains the travel tie for the source locations at the surface to the target point. In the focusing operator, these travel ties are the delays that have to be applied to ensure that the waves generated by the source arrive at the sae tie at the target location. So coparing the observed travel tie with the tie reversed focusing operator allows us to perfor a consistency check. The differential tie shift (DTS) panel shows the travel tie difference between the CFP-gather and the focusing operator. The observed difference can be used to update the focusing operator. We will deonstrate this concept using nuerically odeled data. 3. Modeled data using anisotropic finite difference ethod The technology outlined in the previous paragraphs is deonstrated on nuerically odeled data. The odel consists of a 64 eleent phased array, where all eleents are fired sequentially (see Figure ). j Ø 1 Absorbing boundary 4 6 Figure The odel geoetry, consisting of a 64 eleent phased array and a strongly anisotropic etal with three side-drilled holes. The propagation velocity in the and 9 direction is 9% of that in the 4 direction. The resulting wave field is recorded by all eleents. The ediu is hoogeneous, but strongly anisotropic and contains three side drilled holes. The left and right side of the odel are absorbing regions to avoid reflections fro these boundaries. As reference, the sae geoetry is used to generate an isotropic dataset. Two snapshots of the propagating wave field are shown in Figure 3, on the left hand side for the isotropic case and on the right hand side for the anisotropic case. Coparison clearly shows the effect of the aterial anisotropy. The wave front travels uch faster (about 1% velocity

4 difference) in the 4 direction than in the and 9 direction. Therefore the response fro the side drilled holes gives strong non-hyperbolic events. a) b) Figure 3 Snap shots of the vertical coponent of the wave field, a) isotropic case, b) anisotropic case A full dataset was odeled by firing each eleent separately and recording the wave field using all eleents. Selecting only the pulse-echo traces fro the full dataset, clearly shows the difference between the data fro the isotropic and anisotropic odels. This is shown in FIGURE t, us 1 1 t, us FIGURE 4 Pulse-echo section fro the full data set (diagonal eleents fro the data atrix), a) isotropic case, b) anisotropic case. 4. Data-driven iaging If a conventional iaging algorith is applied to both datasets, aking the assuption that the ediu is isotropic, the iages shown in Figure are obtained. The isotropic iage (Figure a) clearly indicates the three side drilled holes. For reference the position of each side drilled hole is indicated by o. Due to aperture liitations the indication fro the first and third side drill hole are tilted. The side drilled hole on the left hand side, is ainly illuinated fro the right. This explains the tilt of the indication. The sae holds for the side drilled hole on the right hand side, which is ainly illuinated fro the left.

5 The iage using the anisotropic data is quite poor, containing any artifacts. Additionally the side drilled holes are not iaged at their correction locations. Consequently, defects ay be issed in the presence of structural echoes. 1 1 z, z, a) b) Figure Iages assuing a isotropic ediu, a) isotropic dataset, b) anisotropic dataset. The isotropic iage is nearly perfect, while the isotropic iage contains a lot of artifacts. We deonstrate the approach outlined in this paper on the anisotropic dataset. First a target point on the back wall is selected (see Figure 6a). As a first guess, a hyperbolic operator is used, where the arrival tie of the apex equals half the travel tie of the pulse-echo signal. The DTS-panel is shown in Figure 6b for the first iteration. Using an initial operator as explained, part of the DTS panel will be at zero tie, aking it easy to identify the correct event to pick. Clearly the operator is not correct as can be seen fro the non-zero tie difference. Half the tie difference is used to update the focusing operator and after a few iterations the result in Figure 6c is obtained. In that case the event appears at zero traveltie, which indicates that the correct focusing operator has been found The sae procedure is repeated for other points on the back wall and the response fro the side drilled holes. Figure 7 deonstrates the sae approach being applied to the iddle side drilled hole. Again after just a few iterations a flat DTS panels is obtained as illustrated in Figure 7c. The ethod is very fast and can easily be applied in a user interactive fashion. In the current exaple, the ediu is laterally invariant; this akes it fairly straightforward to interpolate the focusing operators to a full set, which can be used to generate an iage. The result of this procedure is shown in Figure 8b. For reference the original iage is shown in Figure 8a. The result shows that we have successfully iaged the three side drilled holes. The resolution in the iage is slightly lower copared to the isotropic case because of the anisotropy; this is due to the fast velocity in the 4 direction causing the diffraction signals to have less curvature and hence yield a lower resolution. 4

6 s τ, us. 1 z, 3 x b) u, a) τ, us Figure 6 Illustration of the focusing operator updating procedure for a point on the backwall, a) shows the initial iage with the target point indicated by x, b) shows the initial DTS-panel and c) shows the final DTS-panel after just a few iterations. c) u, τ, us. z, 1 3 x b) u, a) τ, us Figure 7 Illustration of the focusing operator updating procedure on the iddle side drilled hole, a) shows the initial iage, b) shows the initial DTS-panel and c) shows the final DTSpanel after just a few iterations. c) u,

7 1 1 z, z, a) b) Figure 8 Coparison of original iage and the one obtained by applying the interpolated focusing operators fro the data.. Operator inversion In ore coplicated edia, for exaple an austenitic weld, the operator interpolation procedure is not straightforward. In that case a toographic inversion algorith can be used to invert for the ediu properties using the derived operators. In general the location of the focus point and the ediu properties are unknown. Inverting the focusing operators allows one to estiate both. Figure 9a shows the inverted angular velocity in the ediu. Based on this, a focusing operator table can be calculated as shown in Figure 9b. The resulting iage is shown in Figure 9c. Coparison with Figure 8b shows essentially no difference in iage quality.

8 a) t, us b) Figure 9 Illustration of operator inversion process, a) first the velocity odel is obtained by using an appropriate inversion schee, b) based on the velocity odel a set of focusing operators is calculated. These are then used to construct an iage (c). 6. Conclusions This paper has deonstrated a new technique to deterine focusing operators fro ultrasonic data. The concept was successfully applied to a odeled dataset for a strongly anisotropic ediu. Extracting the focusing operators is a straightforward process, which can be perfored interactively. For laterally invariant edia, the operators can be interpolated very siply. For ore coplicated edia, the operators need to be inverted. This yields a spatially variant velocity field and the velocity odel can then be used to calculate the focusing operators. The proposed ethod does not ake any assuptions regarding the ediu or the wave type. This eans it can also be applied to shear waves or guided waves. Moreover extension to 3D data fro D phased arrays is straightforward. z, c)

9 References 1. A.J. Berkhout, Seisic igration; A. Theoretical aspects, Elsevier sciences publishers, Asterda, A.J. Berkhout, 1997a, Pushing the liits of seisic iaging, part I: Prestack igration in ters of double dynaic focusing: Geophysics, 6, A.J. Berkhout, 1997b, Pushing the liits of seisic iaging, part II: Integration of prestack igration, velocity, estiation, and AVO analysis: Geophysics, 6,