0885–3010/$25.00 © 2011 IEEE 427 IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, . 58, . 2, FEBRUARY 2011 Abstract—Previous studies show that the surface wave transmission (SWT) method is eﬀective to determine the depth of a surface-breaking crack in solid materials. However, near- ﬁeld wave scattering caused by the crack aﬀects the reliability and consistency of surface wave transmission measurements. Prior studies on near-ﬁeld scattering have focused on the case where crack depth h is greater than wavelength λ of surface waves (i.e., h/λ > 1). Near-ﬁeld scattering of surface waves remains not completely understood in the range of h/λ for the SWT method (i.e., 0 ≤ h/λ ≤ 1/3), where the transmission coeﬃcient is sensitive to crack depth change and monotonically decreases with increasing h/λ. In this study, the authors thor- oughly investigated the near-ﬁeld scattering of surface waves caused by a surface-breaking crack using experimental tests and numerical simulations for 0 ≤ h/λ ≤ 1/3. First, the eﬀects of sensor locations on surface wave transmission coeﬃcients across a surface-breaking crack are studied experimentally. Data are collected from Plexiglas and concrete specimens using air-coupled sensors. As a result, the variation of transmission coeﬃcients is expressed in terms of the normalized crack depth (h/λ) as well as the normalized sensor location (x/λ). The va- lidity of ﬁnite element models is also veriﬁed by comparing ex- perimental results with numerical simulations (ﬁnite element method). Second, a series of parametric studies is performed using the veriﬁed ﬁnite element model to obtain more com- plete understanding of near-ﬁeld scattering of surface waves propagating in various solid materials with diﬀerent mechani- cal properties and geometric conditions. Finally, a guideline for selecting appropriate sensor arrangements to reliably obtain the crack depth using the SWT method is suggested. I. I S  wave is a type of stress waves that propa- gates along the surface of a solid. The particle motion amplitude of surface waves exponentially decays with the distance from the free surface boundary. When surface waves propagate across a surface-breaking crack, the low- frequency components of the incident surface waves will transmit to the forward scattering ﬁeld with attenuation, but the high-frequency components will be reﬂected back. This property of surface waves is particularly useful to quantitatively evaluate the depth of a surface-breaking crack in a solid medium [1]. Non-destructive testing (NDT) methods of evaluating the depth of a crack based on surface waves has been extensively investigated since the late 1970s. Kino [2], Auld [3], and Achenbach et al. [4] developed approximate scattering theories applicable to surface waves to evalu- ate surface-breaking or near-surface defects. Tien et al. [5] investigated the near scattering of surface waves from a surface-breaking crack based on the approximate scatter- ing theory developed by Kino [2], and measured reﬂection coeﬃcients of incident surface waves to study the behav- ior of fracture crack extension in ceramics. Jungerman et al. [6] explored reﬂection of surface waves using a pulsed acoustic laser probe to characterize surface defects in an aluminum sample. Cooper et al. [7] experimentally inves- tigated surface waves interacting with a surface-breaking crack using non-contact sensors (laser). Achenbach and his colleagues [8]–[10] obtained analytical solutions for in- vestigating near-ﬁeld scattering of surface waves caused by a surface-breaking crack in solids. They established the relationship between reﬂection and transmission coef- ﬁcients of surface waves and the normalized crack depth (crack depth normalized by wavelength of incident surface waves) based on diﬀraction and scattering of harmonic incident surface waves by a surface-breaking crack in the far-ﬁeld region (i.e., sensors are located far from a crack opening). Previous researchers demonstrated that the transmis- sion coeﬃcient of surface waves is a good indicator to estimate the depth of a surface-breaking crack in solid ma- terials. Yew et al. [11] experimentally obtained the trans- mission coeﬃcients of surface waves Tr and normalized crack depth h/λ relation for a surface-breaking crack in aluminum specimens, in which the incident surface waves were generated by dropping a steel ball on the specimen surface. Cheng and Achenbach [12] successfully veriﬁed the established Tr and h/λ relation [8]–[10] on aluminum specimens using a self-calibrating ultrasonic technique [13]. Recently, Masserey and Mazza [14] veriﬁed that the established Tr and h/λ relation in the studies [8]–[10] is also valid for arbitrary incident waves. For concrete, a het- erogeneous but statistically isotropic material, previous researchers [15]–[17] demonstrated that the NDT method based on surface wave transmission (SWT) measurement was eﬀective to evaluate depth of cracks in concrete, even for tightly closed or ill-deﬁned cracks. Recently, Kee and Zhu [18] improved the test consistency and eﬃciency of the SWT method by using air-coupled sensors. Near-ﬁeld scattering caused by the interaction between surface waves and a surface-breaking crack has been in- vestigated by many researchers [18]–[21]. The authors [18] Eﬀects of Sensor Locations on Air-Coupled Surface Wave Transmission Measurements Across a Surface-Breaking Crack Seong-Hoon Kee and Jinying Zhu Manuscript received May 11, 2010; accepted October 25, 2010. The authors are with the Department of Civil, Architectural, and En- vironmental Engineering, the University of Texas, Austin, TX (e-mail: jyzhu@mail.utexas.edu). Digital Object Identiﬁer 10.1109/TUFFC.2011.1820