Ultrasonic Shear Wave Research Articles

Appraising Kirchhoff approximation theory for the scattering of elastic shear waves by randomly rough defects

Rapid and accurate methods, based on the Kirchhoff approximation (KA), are developed to evaluate the scattering of shear waves by rough defects and quantify the accuracy of this approximation. Defect roughness has a strong effect on the reflection of ultrasound, and every rough defect has a different surface, so standard methods of assessing the sensitivity of inspection based on smooth defects are necessarily limited. Accurately resolving rough cracks in non-destructive evaluation (NDE) inspections often requires shear waves since they have higher sensitivity to surface roughness than longitudinal waves. KA models are attractive, since they are rapid to deploy, however they are an approximation and it is important to determine the range of validity for the scattering of ultrasonic shear waves; this range is found here. Good agreement between KA and high fidelity finite element simulations is obtained for a range of incident/scattering angles, and the limits of validity for KA are found to be much stricter than for longitudinal wave incidence; as the correlation length of rough surfaces is reduced to the order of the incident shear wavelength, a combination of multiple scattering and surface wave mode conversion leads to KA predictions diverging from those of the true diffuse scattered fields.

Association of Pain History and Current Pain With Sagittal Spinal Alignment and Muscle Stiffness and Muscle Mass of the Back Muscles in Middle-aged and Elderly Women.

A cross-sectional study. To investigate the association of low back pain history (LBPH) and LBP with sagittal spinal alignment, stiffness assessed using ultrasonic shear wave elastography, and mass of the back muscle in community-dwelling middle-aged and elderly women. The association of LBPH and LBP with sagittal spinal alignment, stiffness, and mass of the back muscles remains unclear in middle-aged and elderly women. The study comprised 19 asymptomatic middle-aged and elderly women [control (CTR) group], 16 middle-aged and elderly women with LBPH (LBPH group), and 23 middle-aged and elderly women with LBP (LBP group). Sagittal spinal alignment in the standing and prone positions (kyphosis angle in the thoracic spine, lordosis angle in the lumbar spine, and anterior inclination angle in the sacrum) was measured using a Spinal Mouse. The stiffness of the back muscles (lumbar erector spinae and multifidus) in the prone position was measured using ultrasonic shear wave elastography. The mass of the back muscles (thoracic and lumbar erector spinae, lumbar multifidus, and quadratus lumborum) was also measured. Multiple logistic regression analysis with a forward selection method showed that the stiffness of the lumbar multifidus muscle was a significant and independent factor of LBPH. The stiffness of the lumbar multifidus muscle was significantly higher in the LBPH group than in the CTR group. Multiple logistic regression analysis also indicated that lumbar lordosis angle in the standing position was a significant and independent factor of LBP. The lumbar lordosis angle was significantly smaller in the LBP group than in the CTR group. Our results suggest that LBPH is associated with increased stiffness of the lumbar multifidus muscle in the prone position, and that LBP is associated with the decreased lumbar lordosis in the standing position in community-dwelling middle-aged and elderly women.

Static stretching time required to reduce iliacus muscle stiffness

ABSTRACT Static stretching (SS) is an effective intervention to reduce muscle stiffness and is also performed for the iliopsoas muscle. The iliopsoas muscle consists of the iliacus and psoas major muscles, among which the former has a greater physiological cross-sectional area and hip flexion moment arm. Static stretching time required to reduce muscle stiffness can differ among muscles, and the required time for the iliacus muscle remains unclear. The purpose of this study was to investigate the time required to reduce iliacus muscle stiffness. Twenty-six healthy men participated in this study. A 1-min hip extension SS was performed five times. Shear elastic modulus, an index of muscle stiffness, of the iliacus muscle was measured using ultrasonic shear wave elastography before SS and immediately after each SS. One-way repeated analysis of variance showed a statistical effect of time on the shear elastic modulus. A paired t-test with Holm adjustment revealed that the shear elastic moduli after 1–5 SS were statistically lower than that before SS. In addition, the shear elastic modulus after 5 SS was statistically lower than that after 1 SS. The results suggested that the stiffness of the iliacus muscle decreased with 1-min SS and further decreased with 5-min SS.

STUDY OF THE PROPERTIES OF COMPOSITE MATERIALS BASED ON ANTIFRICTION ALLOY B83

The antifriction composite materials (CM) based on a B83 babbit alloy containing silicon carbide (SiC) and modifided shungite (MS) particles have been fabricated by hot pressing. The matrix powder was prepared using a planetary ball mill for processing chips obtained by machining of cast aabbitt. The resulting powder was sieved on a sieve analyzer. Powder mixtures for pressing were prepared by mechanical alloying in a planetary mill for 2 h at a stirring speed of 300 rpm. Composite semi-product was obtained by pressing the obtained powder mixtures on an ОМА mechanical press (P max = 150 kN) at pressure of 320 ± 5 MPa. Semi-products were heated in a muffle furnace in a mold at a temperature up to 300°C, kept at this temperature for 30 min and then pressed. We have shown that CM obtained using methods of powder metallurgy exhibit increased wear resistance at comparable values of the friction coefficient compared to the same properties of a cast alloy. Local elastic moduli of the obtained samples have been determined using the laser optoacoustic method based on the measurements of the phase velocities of thermo-optically excited longitudinal and shear ultrasonic waves. We have shown that B83-based CM containing MS (0.5 wt.%) and SiC (3 wt.%) can be recommended as an alternative to a B83 cast alloy due to the higher wear resistance compared to cast babbit. The friction surface of this composite material reveals the sliding areas and friction relief less distinct compared to the cast alloy.

Effect of Rest Duration Between Static Stretching on Passive Stiffness of Medial Gastrocnemius Muscle In Vivo.

In clinical and sports settings, static stretching (SS) is usually performed to increase range of motion (ROM) and decrease passive muscle stiffness. Recently, the shear elastic modulus was measured by ultrasonic shear wave elastography as an index of muscle stiffness. Previous studies reported that the shear elastic modulus measured by ultrasound shear wave elastography decreased after SS, and the effects of SS on shear elastic modulus were likely affected by rest duration between sets of SS. To investigate the acute effects of SS with different rest durations on ROM and shear elastic modulus of gastrocnemius and to clarify whether the rest duration between sets of SS decreases the shear elastic modulus. A randomized, repeated-measures experimental design. University laboratory. Sixteen healthy males volunteered to participate in the study (age 21.3 [0.8] y; height 171.8 [5.1]cm; weight 63.1 [4.5]kg). Each participant underwent 3 different rest interval durations during SS (ie,long rest duration: 90s; normal rest duration: 30s; and short rest duration: 10s). This SS technique was repeated 10 times, thus lasting a total of 300 seconds with different rest durations in each protocol. The dorsiflexion ROM and shear elastic modulus were measured before and after SS. Our results revealed that dorsiflexion ROM and shear elastic modulus were changed after 300-second SS; however, no effects of the rest duration between sets of SS were observed. In terms of decreasing the shear elastic modulus, clinicians and coaches should not focus on the rest duration when SS intervention is performed.

Abdominal girth as an index of muscle tension during abdominal hollowing: Selecting the optimal training intensity for the transversus abdominis muscle

The abdominal hollowing technique is used for training the transversus abdominis (TrA). However, the optimal intensity of hollowing is still unclear. The objective of the present study is to verify the validity of estimating the tension of the TrA by measuring the girth of the abdomen with a tape and to determine the optimum intensity of hollowing to effectively train the TrA. Sixteen healthy males performed hollowing with an intensity of 0%, 25%, 50%, 75%, and 100%, estimated from the girth of the abdomen. The shear elastic modulus was measured for the rectus abdominis (RA), external oblique (EO), internal oblique (IO), and TrA at all intensities via ultrasonic shear wave elastography. The shear elastic modulus was considered as the index of the tension of the abdominal muscles at each intensity, and the ratio of the TrA to RA, EO, and IO respectively was calculated as the index of TrA selectivity. As the intensity of hollowing increased, the girth of abdomen decreased and tension of all the four muscles increased. The ratio of TrA to the RA, EO, and IO did not exhibit a significant variation among hollowing intensities of 25% to 100%. It is rational to estimate the tension of the TrA by measuring the girth of the abdomen. Moreover, considering both TrA contraction intensity and selectivity, abdominal hollowing performed at maximum intensity was effective for the maximum contraction training of the TrA.

Acoustic Structural Analysis of Steel Samples Loaded with Rotational Bending During Fatigue Tests

С целью исследования влияния накопленной поврежденности металла на скорость ультразвуковых сдвиговых и рэлеевских волн образцы стального пруткового проката подвергли циклическому нагружению по схеме консольного изгиба с вращением. Представлены результаты измерения скорости ультразвуковых волн (сдвиговых и рэлеевских) в стальных прутках при малоцикловой усталости под воздействием циклических нагрузок. Исследованы образцы прутков марки стали 40Х в состоянии поставки и после отжига при температуре 700 оС в течение 30 мин. Длина прутков - 270 мм, диаметр - 10 и 19 мм. Циклические нагружения консольным изгибом обеспечивались с помощью специально разработанной установки для испытаний на усталость, в которой пруток одной стороной зажимался в патроне машины, обеспечивающей вращение, на другой стороне через подшипник подвешивался груз. Оценивались скорости сдвиговых волн в направлениях поперечного сечения прутка и рэлеевских волн по огибающей цилиндрической поверхности прутка в зоне максимальных напряжений. Возбуждение и прием волн осуществляли электромагнитно-акустическим способом. Для оценки скорости сдвиговых (поперечных) и рэлеевских волн использовался метод многократных отражений, соответственно, по сечению и огибающей прутка. Представлены результаты изменения скорости в прутках при увеличении консольной нагрузки и числа циклов. Найдено, что скорость сдвиговой волны в прутке максимально уменьшается в зоне максимальных напряжений. При нагрузках, составляющих 60 % от предела текучести, в образцах наблюдается резкое снижение скорости при 300000 циклах. Изменение структуры металла после отжига приводит к снижению числа циклов, после которого происходит резкое изменение скорости волн. Коэффициент Пуассона, рассчитанный по скоростям сдвиговых и рэлеевских волн, также изменяется с ростом числа циклов и позволяет учесть изменение диаметра прутка в процессе испытаний. Проведенные эксперименты по исследованию влияния циклических нагрузок прутков дают хорошие информативные данные по усталости в зависимости от термической обработки и структурных изменений материала. Возможность реализации электромагнитно-акустического метода контроля на многократных отражениях позволяет существенно повысить чувствительность к микродефектам при анализе сигнала на дальних отражениях и обеспечить высокую точность определения скорости волн.

1061 - A new method of quantitatively measuring penile erection hardness in erectile dysfunction patients: Real-time ultrasonic shear wave elastography

1061 - A new method of quantitatively measuring penile erection hardness in erectile dysfunction patients: Real-time ultrasonic shear wave elastography

Effects of the trunk position on muscle stiffness that reflects elongation of the lumbar erector spinae and multifidus muscles: an ultrasonic shear wave elastography study.

The present study aimed to clarify the effects of the trunk position on muscle stiffness that reflects elongation of the lumbar erector spinae and lumbar multifidus muscles using ultrasonic shear wave elastography (SWE). The study included ten healthy men. The shear elastic modulus of the left lumbar erector spinae and lumbar multifidus muscles were evaluated using ultrasonic SWE. Measurement postures for the left lumbar erector spinae muscle were (1) prone position (Rest), (2) sitting position with the trunk flexed (Flexion), (3) the Flexion position adding right trunk lateral flexion (Flexion-Lateral Flexion), and (4) the Flexion position adding right trunk rotation (Flexion-Rotation 1). The left lumbar multifidus muscle were measured in positions (1)-(3), and (5) the Flexion position adding left trunk rotation (Flexion-Rotation 2). The shear elastic modulus of the lumbar erector spinae muscle in the Flexion-Lateral Flexion position was significantly higher than that in the Rest, Flexion, or Flexion-Rotation 1 positions. Shear elastic modulus of the lumbar multifidus muscle was similar in the Flexion, Flexion-Lateral Flexion, and Flexion-Rotation 2 positions, but significantly lower in the Rest position. The results of the present study suggest that the lumbar erector spinae muscle is stretched effectively in the position adding trunk contralateral lateral flexion to flexion. The results also indicate that the lumbar multifidus muscle, which does not appear to be affected by adding trunk contralateral lateral flexion or ipsilateral rotation to flexion, is stretched effectively in the trunk flexion position.

Study of a Welded Joint of 12Kh18N10T Steel Using Acoustic and Magnetic Methods

The paper presents results from studies on the influence of plastic deformation on magnetic and acoustic characteristics of a welded joint material of 12Kh18N10T (analogue AISI 321) austenitic steel. We have shown that an inhomogeneous structure in the heat-affected zone causes a nonuniform distribution of acoustic parameters and magnetic properties of the welded joint material. The formation of the martensitic phase occurs upon plastic deformation, which influences the properties of the whole material and has elastic moduli differing from that of the original austenitic phase. The increase in the volume fraction of martensite leads to the decrease in the elastic moduli of the material and, as a consequence, to the decrease of ultrasonic waves velocity. The variation of ultrasonic waves velocities leads to significant errors upon measurements of the material parameters under study, for instance, of a sheet thickness using ultrasonic thickness measurement. The formation of martensite changes also the magnetic properties of the material. We have found the dependence of the shear ultrasonic wave velocity on a parameter governed by the change in the phase composition of the austenitic steel upon plastic deformation. We have developed an algorithm for the determination of the thickness of the welded joint metal undergoing pressure forming and plastic deformation upon operation of constructions. We have shown that the additional measurement using the magnetic method of the parameter governed by the change in the phase composition of the steel upon deformation substantially decreases the errors of the thickness measurement of the welded joint metal.

Thermomechanical model for monotonic and cyclic loading of PEEK

An internal state variable (ISV) model for polyether ether ketone (PEEK) is developed to capture experimental measurements conducted below its glass transition temperature. The model is based on the response of two relaxing components put in parallel, one having a back stress response that softens with plastic flow. This softening allows reproducing both monotonic and cyclic loading, and is possibly associated with detangling, melting of network junctions, and/or change in crystallinity. The resulting model, which is thermodynamic and multidimensional, was used to capture the response of PEEK 450G using thermal expansion (23 °C to 120 °C), heat capacity (−40 °C to 140 °C), monotonic extension and compression (−85 °C to 150 °C; 0.0001 s−1 to 3000 s−1; strains up to 40–80%), equilibrium stress measurements in compression (23 °C to 120 °C; strains up to 60%), and ultrasonic longitudinal and shear wave speed measurements along and transverse to the directions of compression (23 °C to 120 °C; up to 50% plastic compression). The model is compared to the response under monotonic and cyclic shear and internal dissipation is assessed using the equivalent adiabatic temperature rise.

Non-invasive Quantitative Assessment of Muscle Force Based on Ultrasonic Shear Wave Elastography

The objective of this study was to investigate the feasibility of using shear wave elastography (SWE) to indirectly measure passive muscle force and to examine the effects of muscle mass and scan angle. We measured the Young's moduli of 24 specimens from six muscles of four swine at different passive muscle loads under different scan angles (0°, 30°, 60° and 90°) using SWE. Highly linear relationships between Young's modulus E and passive muscle force F were found for all 24 muscle specimens at 0o scan angle with coefficients of determination R2 ranging from 0.984 to 0.999. The results indicate that the muscle mass has no significant effect on the muscle E–F relationship, whereas E–F linearity decreases disproportionately with increased scan angle. These findings suggest that SWE, when carefully applied, can provide a highly reliable tool to measure muscle Young's modulus, and could be used to assess the muscle force quantitatively.

Construction of left atrial appendage three-dimensional model based on transesophageal echocardiography and its value in preoperative simulated left atrial appendage closure

Objective To evaluate the accuracy of simulated operation before the left atrial appendage (LAA) occlusion by filed LAA model with soft materials, which is based on transesophageal three-dimensional echocardiography (3D-TEE). Methods Silica and hydrogel were mixed to imitate cardiac tissue. Silica and hydrogel mixed materials, silica and Tangoplus were subjected to mechanical detection and ultrasonic shear wave elastography (SWE). The preoperative and postoperative 3D-TEE image processing was performed on 21 patients undergoing LAA occlusion. The silica and hydrogel LAA 3D model, silicone model and Tangoplus model were acquired to evaluate the accuracy of 3D model. LAA closure was simulated using the 3D models and the compression ratio of the device in models was compared with the value measured in operation. Results The silica and hydrogel mixed materials were successfully prepared. The elastic modulus and stress-strain curve were closer to the myocardial tissue. Twenty-one 3D printing models of three materials were obtained in 21 patients based on 3D-TEE images.There was no significant difference in the anchor zone between the 3D model and 3D-TEE (P>0.05). The 3D model measurements were consistent with the 3D-TEE measurements. The compression ratios of the decive in the 3D models of all three materials were greater than those measured in operation, and the compression ratio of the device in the 3D model of silica and hydrogel materials had a better correlation with that measured in operation (r=0.900, P<0.01). Conclusions The 3D model of LAA made of silica and hydrogel material based on 3D-TEE can improve the accuracy of the LAA occlusion simulation, also can optimize the preparation of LAA occlusion. Key words: Echocardiography, transesophageal, three-dimensional; Three-dimensional printing; Left atrial appendage; Soft printing material

Effective stretching position for the supraspinatus muscle evaluated by shear wave elastography in vivo

Stretching is useful for increasing flexibility in clinical and athletic situations. Although several authors have recommended various stretching techniques for the supraspinatus muscle, there is no consensus on the effective stretching position owing to a lack of quantitative analysis in vivo. This study used ultrasonic shear wave elastography in vivo to verify the effective stretching positions for the supraspinatus muscle. The study participants were 15 healthy male volunteers. The shear elastic modulus, used as the index of supraspinatus muscle elongation, was computed using ultrasonic shear wave elastography. The shear elastic modulus was measured at neutral position and maximum internal rotation in 9 positions: 0° elevation, 90° abduction, 90° flexion, maximum extension, maximum horizontal adduction at 45° and 90° elevation, and maximum horizontal abduction at 20°, 45°, and 90° elevation. The shear elastic moduli were significantly greater in maximum internal rotation at maximum horizontal abduction with 45° and 90° elevation and maximum internal rotation at maximum extension than those in the other positions. There were no significant differences in the shear elastic moduli among these 3 positions. This study demonstrated that maximum internal rotation at maximum extension, maximum internal rotation at maximum horizontal abduction with 90° elevation, and maximum internal rotation at maximum horizontal abduction with 45° elevation are effective stretching positions for the supraspinatus muscle.

Nondestructive analysis techniques for freeze-thaw damage detection in concrete slabs using shear waves

Freeze-thaw damage in concrete structures is a serious issue for infrastructure in cold regions. Accurate detection of this type of damage at early stages allows for the selection of optimum strategies for preservation and rehabilitation activities. This paper explores the feasibility of utilizing ultrasonic shear wave technology, called MIRA, for quantification of damage in concrete slabs for the detection of freeze-thaw damage. Four slabs with varying levels of freeze-thaw damage were tested and two analysis techniques were developed to characterize the damage present. These methods involve the formulation of reconstruction images to analyze the subsurface condition, as well as the creation of a numerical index based upon recorded shear wave signal characteristics. The results of both analyses showed agreement both with each other and with the visual survey assessments for detection of freeze-thaw damage. However, the methods were also able to detect damage in portions of the slab where no visual cracks were observed. These techniques showed promise for an accurate nondestructive quantification of the extent of freeze-thaw damage, or similar damage manifestations, in concrete structures. Advantages of the methods include their applicability on in-situ concrete infrastructure for determining real-time concrete condition, without requiring previous measurements for comparative purposes.

Ultrasonic shear wave reflectometry applied to the determination of the shear moduli and viscosity of a viscoelastic bitumen

Ultrasonic shear wave reflectometry is widely used in process control to measure the dynamic shear viscosities of Newtonian liquids. We apply the technique to study the temperature dependence of produced bitumen: a non-Newtonian ultra-heavy 6° API hydrocarbon with a room temperature viscosity of ∼103 Pa·s. The experimental apparatus employs a delay line made of polyetheretherketone (PEEK) whose shear impedance more closely matches that of the bitumen allowing for greater sensitivity but at the cost of long equilibration wait times. The temperature dependent values of the complex shear modulus and consequent estimates of the steady flow shear viscosity both follow close to an Arrhenius-like behaviour over the range of 10 °C–50 °C, but there are significant discrepancies between the ultrasonic and more conventional spindle viscosities. These may reflect differences between the particle displacements, the strains, and the strain rates associated with each measurement technique. It is in the nature of bitumen to shear thin at high shear rate using ultrasonic technique. Regardless, these measurements do show that the shear wave reflectometry does provide information on the changes in the viscoelastic bitumen with temperature that may be useful in for purposes of its monitoring during production and processing.

Contribution of the shear wave ultrasonic reflectometry to the stickiness measurements

Today, non-invasive quantification of the adhesion of a deposit to a surface is always a challenge and, unfortunately, few tools are available in this area. This is an obstacle, in several industrial processes, to the identification of conditions limiting the fouling and to the establishment of eco-efficient cleaning strategies.In this paper, a non-invasive ultrasonic technique was developed in the aim of characterizing the adhesion of viscoelastic fluids or solid deposited on a substrate. We adopted the idea that the more a deposit is difficult to clean the more adherent it is. From this point of view the value of the reflection coefficient of an ultrasonic shear wave informs us about the adhesion of the deposit on a surface.A large bibliography on the adhesion measurement is given. Then the principle of ultrasonic test is presented and cares required for the measurement of the reflection coefficient are widely discussed. The ultrasonic reflection coefficients obtained with different controlled samples covering a wide range of interfaces (liquid/substrate, solid/substrate) are presented and compared with other indicators of adhesion. All the data on various samples showed that the ultrasonic test is a tool to discriminate non-destructively a large range of interface quality, allowing ranking according to the adhesive strength.

Material Damage Evolution for Plain and Steel-Fiber-Reinforced Concrete Under Unconfined Compression Loading by Dynamic Ultrasonic Tests

This paper summarizes the results of a research aimed at assessing the damage of plain and steel-fiber-reinforced concrete when using ultrasonic compression and shear wave velocities. The ultrasonic waves and the axial compression loading were oriented to the same direction in order to track the damage progress during several loading steps. The concrete damage was monitored based on the evolution of the dynamic mechanical properties. The experimental program included 18 cylindrical specimens from six different mixtures that were cast by using 0, 0.3 and 0.5% fiber volume contents. Quantitative models were established linking the axial loads, the wave velocities, the dynamic Young’s and shear moduli, the Poisson’s ratio and a damage index.

In silico simulation of liver crack detection using ultrasonic shear wave imaging

BackgroundLiver trauma is an important source of morbidity and mortality worldwide. A timely detection and precise evaluation of traumatic liver injury and the bleeding site is necessary. There is a need to develop better imaging modalities of hepatic injuries to increase the sensitivity of ultrasonic imaging techniques for sites of hemorrhage caused by cracks. In this study, we conduct an in silico simulation of liver crack detection and delineation using an ultrasonic shear wave imaging (USWI) based method.MethodsWe simulate the generation and propagation of the shear wave in a liver tissue medium having a crack using COMSOL. Ultrasound radio frequency (RF) signal synthesis and the two-dimensional speckle tracking algorithm are applied to simulate USWI in a medium with randomly distributed scatterers. Crack detection is performed using the directional filter and the edge detection algorithm rather than the conventional inversion algorithm. Cracks with varied sizes and locations are studied with our method and the crack localization results are compared with the given crack.ResultsOur pilot simulation study shows that, by using USWI combined with a directional filter cum edge detection technique, the near-end edge of the crack can be detected in all the three cracks that we studied. The detection errors are within 5%. For a crack of 1.6 mm thickness, little shear wave can pass through it and the far-end edge of the crack cannot be detected. The detected crack lengths using USWI are all slightly shorter than the actual crack length. The robustness of our method in detecting a straight crack, a curved crack and a subtle crack of 0.5 mm thickness is demonstrated.ConclusionsIn this paper, we simulate the use of a USWI based method for the detection and delineation of the crack in liver. The in silico simulation helps to improve understanding and interpretation of USWI measurements in a physical scattered liver medium with a crack. This pilot study provides a basis for improved insights in future crack detection studies in a tissue phantom or liver.

Analytical reverse time migration: An innovation in imaging of infrastructures using ultrasonic shear waves

The emergence of ultrasonic dry point contact (DPC) transducers that emit horizontal shear waves has enabled efficient collection of high-quality data in the context of a nondestructive evaluation of concrete structures. This offers an opportunity to improve the quality of evaluation by adapting advanced imaging techniques. Reverse time migration (RTM) is a simulation-based reconstruction technique that offers advantages over conventional methods, such as the synthetic aperture focusing technique. RTM is capable of imaging boundaries and interfaces with steep slopes and the bottom boundaries of inclusions and defects. However, this imaging technique requires a massive amount of memory and its computation cost is high. In this study, both bottlenecks of the RTM are resolved when shear transducers are used for data acquisition. An analytical approach was developed to obtain the source and receiver wavefields needed for imaging using reverse time migration. It is shown that the proposed analytical approach not only eliminates the high memory demand, but also drastically reduces the computation time from days to minutes.