Shear Wave Source Research Articles

Shear wavelength estimation based on inverse filtering and multiple-point shear wave generation

Elastography provides important diagnostic information because tissue elasticity is related to pathological conditions. For example, in a mammary gland, higher grade malignancies yield harder tumors. Estimating shear wave speed enables the quantification of tissue elasticity imaging using time-of-flight. However, time-of-flight measurement is based on an assumption about the propagation direction of a shear wave which is highly affected by reflection and refraction, and thus might cause an artifact. An alternative elasticity estimation approach based on shear wavelength was proposed and applied to passive configurations. To determine the elasticity of tissue more quickly and more accurately, we proposed a new method for shear wave elasticity imaging that combines the shear wavelength approach and inverse filtering with multiple shear wave sources induced by acoustic radiation force (ARF). The feasibility of the proposed method was verified using an elasticity phantom with a hard inclusion.

Prediction of peak ground acceleration using ϵ-SVR, ν-SVR and Ls-SVR algorithm

ABSTRACTIn this paper, a prediction model is developed using support vector machine for forecasting the parameter associated with ground motion of a seismic signal. The prediction model is developed using three learning algorithms, ϵ-support vector regression, ν-support vector regression and least square-support vector regression (Ls-SVR) for forecasting peak ground acceleration (PGA), a parameter associated with ground motion of a seismic signal. The prediction model is developed for each of the algorithms with different kernel functions, namely linear kernel, polynomial kernel and radial basis function kernel. The ground motion parameter is related to four seismic parameters, namely faulting mechanism, average soil shear wave velocity, earthquake magnitude and source to site distance. The database used for modelling is NGA flatfile released by Pacific Earthquake Engineering Research Center. The experimental results show that the optimal prediction model for forecasting PGA is Ls-SVR with RBF kernel. It is observed that the developed prediction model is better compared to the existing conventional models and benchmark models in the same database. This paper further compares the three variations of SVR algorithm for ground motion parameter prediction model. The learning effectiveness of each algorithm is measured in terms of accuracy, testing error and overfitness measure.

Seismic characterization and monitoring of a deep CO2 storage reservoir with 3D VSP using direct shear waves

We show a low-cost option for shear wave imaging of CO2 storage reservoirs that utilizes seismic waves that have been ignored by reflection seismologists for decades. These overlooked waves are direct-S waves generated by vertical-displacement vibrators and explosive sources. Shear waves are known to be helpful for detecting fractures and subtle faults which is critical for evaluating of CO2 storage capacity and sealing properties of the caprock. Utilizing direct-S waves produced by P-wave sources provides these benefits with no need to deploy special shear-wave sources. In addition, the SV-P mode, which is the upgoing P-wave produced by SV-to-P conversion, makes it possible to utilize S-wave attributes with data recorded by vertical geophones only.We developed a processing workflow to extract SV-SV and SV-P seismic modes from 3D VSP data acquired over a CO2 storage reservoir at Decatur, Illinois and tested these modes for seismic imaging and monitoring of the reservoir. In addition, we inspected an SH-SH mode that appeared interpretable in our data. We observed that direct-S images were consistent with traditional VSP direct-P images and calibration synthetic seismograms. A joint analysis of all available seismic modes allowed a constrained interpretation of faults within the reservoir. Direct-S waves appeared to not be advantageous for CO2 plume growth monitoring in the Decatur project. The SV-P mode demonstrated low sensitivity to CO2 concentration. The time-lapse difference for the SV-SV mode was uninterpretable due to the low signal-to-noise ratio of that mode.

Acoustic time reversal in granular media

In a non-dissipative medium, the wave equation is symmetric in time. Therefore, for every wave diverging from a pulsed source, there exists a wave that retraces all its original paths in a reverse order and converges at the original source. In the early nineties, M. Fink proposed a method for generating such a time-reversed wave. This method was first tested with ultrasound and then successfully extended to other types of waves such as microwaves, water waves, and even in optics. Several studies have shown that time reversal wave focusing is very robust to disorder. Here, we investigate time reversal (TR) of elastic waves propagating in fragile granular media consisting of glass beads under static compression. Pulsed elastic waves transmitted from a compression or a shear wave source are measured, time reversed, and back-propagated. The ability of the time-reversed wave to focus at the initial source is checked as a function of the source amplitude. We find that TR of the ballistic coherent wave is very robust to perturbations but provides poor resolution. By contrast, the short-wavelength scattered waves offer a finer TR focusing but are sensitive to rearrangements induced by the forward propagation wave itself: at large source amplitudes, time reversal focusing is broken, due to sound-induced rearrangements but without visible grain motion. Experimental results are confronted with predictions from a numerical model in which the propagation medium is modelled by a percolating network of masses interacting via linear springs.

On the generalization to swirling flows of Lighthill’s eighth-power law: Part I: Waves in axisymmetric sheared and swirling isentropic flows

The Lighthill–Proudman theory of sound generation by turbulence, inhomogeneities, and dissipation in a medium at rest is extended to an axisymmetric mean flow with (i) arbitrary unidirectional shear velocity profile and (ii) arbitrary angular velocity of rotation, both depending only on the radius and also (iii) isentropic conditions. The forced acoustic-vortical wave equation is obtained in space-time and in frequency-wavenumber domain retaining the radial dependence. The wave operator describes the propagation of coupled acoustic-vortical waves including the special cases of potential vortex and rigid-body swirl. The forcing term specifies the compressive, shear, and swirl wave sources that model the generation of acoustic-vortical waves (part II).

The diffraction of Rayleigh waves by a fluid-saturated alluvial valley in a poroelastic half-space modeled by MFS

Two dimensional diffraction of Rayleigh waves by a fluid-saturated poroelastic alluvial valley of arbitrary shape in a poroelastic half-space is investigated using the method of fundamental solutions (MFS). To satisfy the free surface boundary conditions exactly, Green’s functions of compressional (PI and PII) and shear (SV) wave sources buried in a fluid-saturated poroelastic half-space are adopted. Next, the procedure for solving the scattering wave field is presented. It is verified that the MFS is of excellent accuracy and numerical stability. Numerical results illustrate that the dynamic response strongly depends on such factors as the incident frequency, the porosity of alluvium, the boundary drainage condition, and the valley shape. There is a significant difference between the diffraction of Rayleigh waves for the saturated soil case and for the corresponding dry soil case. The wave focusing effect both on the displacement and pore pressure can be observed inside the alluvial valley and the amplification effect seems most obvious in the case of higher porosity and lower frequency. Additionally, special attention should also be paid to the concentration of pore pressure, which is closely related to the site liquefaction in earthquakes.

A multiresolution approach to shear wave image reconstruction

Shear wave imaging techniques build maps of local elasticity estimating the local group velocity of induced mechanical waves. Velocity estimates are formed using the time delay in the motion profile of the medium at two or more points offset from the shear wave source. Because the absolute time-of-flight between any pair of locations scales with the distance between them, there is an inherent trade-off between robustness to time-of-flight errors and lateral spatial resolution based on the number and spacing of the receive points used for each estimate. This work proposes a method of using the time delays measured between all combinations of locations to estimate a noise-robust, high-resolution image. The time-of-flight problem is presented as an overdetermined system of linear equations that can be directly solved with and without spatial regularization terms. Finite element method simulations of acoustic radiation force-induced shear waves are used to illustrate the method, demonstrating superior contrast-to-noise ratio and lateral edge resolution characteristics compared with linear regression of arrival times. This technique may improve shear wave imaging in situations where time-of-flight noise is a limiting factor.

Modelling the impulse diffraction field of shear waves in transverse isotropic viscoelastic medium

The generation of shear waves from an ultrasound focused beam has been developed as a major concept for remote palpation using shear wave elastography (SWE). For muscular diagnostic applications, characteristics of the shear wave profile will strongly depend on characteristics of the transducer as well as the orientation of muscular fibers and the tissue viscoelastic properties. The numerical simulation of shear waves generated from a specific probe in an anisotropic viscoelastic medium is a key issue for further developments of SWE in fibrous soft tissues. In this study we propose a complete numerical tool allowing 3D simulation of a shear wave front in anisotropic viscoelastic media. From the description of an ultrasonic transducer, the shear wave source is simulated by using Field’s II software and shear wave propagation described by using the Green’s formalism. Finally, the comparison between simulations and experiments are successively performed for both shear wave velocity and dispersion profile in a transverse isotropic hydrogel phantom, in vivo forearm muscle and in vivo biceps brachii.

Multi-source and multi-directional shear wave generation with intersecting steered ultrasound push beams.

Elasticity imaging is becoming established as a means of assisting in diagnosis of certain diseases. Shear wave-based methods have been developed to perform elasticity measurements in soft tissue. Comb-push ultrasound shear elastography (CUSE) is one of these methods that apply acoustic radiation force to induce the shear wave in soft tissues. CUSE uses multiple ultrasound beams that are transmitted simultaneously to induce multiple shear wave sources into the tissue, with improved shear wave SNR and increased shear wave imaging frame rate. We propose a novel method that uses steered push beams (SPB) that can be applied for beam formation for shear wave generation. In CUSE beamforming, either unfocused or focused beams are used to create the propagating shear waves. In SPB methods we use unfocused beams that are steered at specific angles. The interaction of these steered beams causes shear waves to be generated in more of a random nature than in CUSE. The beams are typically steered over a range of 3 to 7° and can either be steered to the left (-θ) or right (+θ).We performed simulations of 100 configurations using Field II and found the best configurations based on spatial distribution of peaks in the resulting intensity field. The best candidates were ones with a higher number of the intensity peaks distributed over all depths in the simulated beamformed results. Then these optimal configurations were applied on a homogeneous phantom and two different phantoms with inclusions. In one of the inhomogeneous phantoms we studied two spherical inclusions with 10 and 20 mm diameters, and in the other phantom we studied cylindrical inclusions with diameters ranging from 2.53 to 16.67 mm. We compared these results with those obtained using conventional CUSE with unfocused and focused beams. The mean and standard deviation of the resulting shear wave speeds were used to evaluate the accuracy of the reconstructions by examining bias with nominal values for the phantoms as well as the contrast-to-noise ratio in the inclusion phantom results. In general the contrast-to-noise ratio (CNR) was higher and the bias was lower using the SPB method compared with the CUSE realizations except in the largest inclusions. In the cylindrical inclusion with 10.4 mm diameter, the CNR in CUSE methods ranged between 18.52 and 22.02 and the bias ranged between 5.50 and 11.12%, whereas for SPB methods provided CNR values between 23.07 and 48.90 and bias values between 3.78 and 9.22%. In a smaller cylindrical inclusion with diameter of 4.05 mm, CUSE methods gave CNR between 14.69 and 22.28 and bias ranging between 28.95 and 29.28%, whereas the SPB methods provided CNR values between 16.7 and 25.2 and bias values varying from 25.54 to 30.44%. The SPB method provides a flexible framework to produce shear wave sources that are widely distributed within the field-of-view for robust shear wave speed imaging.

Analysis of rapid multi-focal-zone ARFI imaging.

Acoustic radiation force impulse (ARFI) imaging has shown promise for visualizing structure and pathology within multiple organs; however, because the contrast depends on the push beam excitation width, image quality suffers outside of the region of excitation. Multi-focal-zone ARFI imaging has previously been used to extend the region of excitation (ROE), but the increased acquisition duration and acoustic exposure have limited its utility. Supersonic shear wave imaging has previously demonstrated that through technological improvements in ultrasound scanners and power supplies, it is possible to rapidly push at multiple locations before tracking displacements, facilitating extended depth of field shear wave sources. Similarly, ARFI imaging can utilize these same radiation force excitations to achieve tight pushing beams with a large depth of field. Finite element method simulations and experimental data are presented, demonstrating that single- and rapid multi-focal-zone ARFI have comparable image quality (less than 20% loss in contrast), but the multi-focal-zone approach has an extended axial region of excitation. Additionally, as compared with single-push sequences, the rapid multi-focalzone acquisitions improve the contrast-to-noise ratio by up to 40% in an example 4-mm-diameter lesion.

Two-dimensional shear-wave elastography on conventional ultrasound scanners with time-aligned sequential tracking (TAST) and comb-push ultrasound shear elastography (CUSE).

Two-dimensional shear-wave elastography presents 2-D quantitative shear elasticity maps of tissue, which are clinically useful for both focal lesion detection and diffuse disease diagnosis. Realization of 2-D shear-wave elastography on conventional ultrasound scanners, however, is challenging because of the low tracking pulse-repetition-frequency (PRF) of these systems. Although some clinical and research platforms support software beamforming and plane-wave imaging with high PRF, the majority of current clinical ultrasound systems do not have the software beamforming capability, which presents a critical challenge for translating the 2-D shear-wave elastography technique from laboratory to clinical scanners. To address this challenge, this paper presents a time-aligned sequential tracking (TAST) method for shear-wave tracking on conventional ultrasound scanners. TAST takes advantage of the parallel beamforming capability of conventional systems and realizes high-PRF shear-wave tracking by sequentially firing tracking vectors and aligning shear wave data in the temporal direction. The comb-push ultrasound shear elastography (CUSE) technique was used to simultaneously produce multiple shear wave sources within the field-of-view (FOV) to enhance shear wave SNR and facilitate robust reconstructions of 2-D elasticity maps. TAST and CUSE were realized on a conventional ultrasound scanner. A phantom study showed that the shear-wave speed measurements from the conventional ultrasound scanner were in good agreement with the values measured from other 2-D shear wave imaging technologies. An inclusion phantom study showed that the conventional ultrasound scanner had comparable performance to a state-of-the-art shear-wave imaging system in terms of bias and precision in measuring different sized inclusions. Finally, in vivo case analysis of a breast with a malignant mass, and a liver from a healthy subject demonstrated the feasibility of using the conventional ultrasound scanner for in vivo 2-D shear-wave elastography. These promising results indicate that the proposed technique can enable the implementation of 2-D shear-wave elastography on conventional ultrasound scanners and potentially facilitate wider clinical applications with shear-wave elastography.

On the source-frequency dependence of fracture-orientation estimates from shear-wave transmission experiments

Shear-wave propagation through anisotropic fractured or cracked media can provide valuable information about these fracture swarms and their orientations. The main goal of this work is to recover information about fracture orientation based on the shear waveforms (S-waveforms). For this study, we carried out ultrasonic S-wave measurements in a synthetic physical model made of epoxy resin (isotropic matrix proxy), with small cylindrical rubber strips as inclusions (artificial cracks) inserted in it to simulate a homogeneous anisotropic medium. In these experiments, we used low, intermediate, and high frequency shear-wave sources, with frequencies 90, 431, and 840kHz. We integrated and interpreted the resulting S-wave seismograms, cross-correlation panels and anisotropic parameter-analysis curves. We were able to estimate the crack orientation in single-orientation fracture zones. The high frequency peaks associated with scattered S-waves provided interpretable information about the fracture orientations when the propagation direction was parallel to the fracture plane. The analysis was possible utilizing results from frequency-versus-polarization-angle curves. Moreover, we applied a bandpass filtering process to the intermediate and high frequency seismograms in order to obtain low frequency seismograms. A spectral analysis using frequency–wavenumber (F–K) spectra supports this filtering process. The results obtained using an analysis of cross-correlograms and the Thomsen parameter γ extracted from filtered high-frequency data were quite similar to those obtained using a low-frequency source. This highlighted the possibility of using less expensive high-frequency sources to recover information about the fracture set.

Borehole seismoelectric logging using a shear-wave source: Possible application to CO2 disposal?

The behaviour of CO2 deposition sites – and their surroundings – during and after carbon dioxide injection has been matter of study for several years, and several geophysical prospection techniques like surface and crosshole seismics, geoelectrics, controlled source electromagnetics among others, have been applied to characterize the behaviour of the gas in the reservoirs. Until now, Seismolectromagnetic wave conversions occurring in poroelastic media via electrokinetic coupling have not been tested for this purpose. In this work, by means of numerical experiments using Pride's equations – extended to deal with partial saturations – we show that the seismoelectric and seismomagnetic interface responses (IR) generated at boundaries of a layer containing carbon dioxide are sensitive to its CO2 content. Further, modeling shear wave sources in surface to borehole seismoelectric layouts and employing two different models for the saturation dependence of the electrokinetic coefficient, we observe that the IR are sensitive to CO2 saturations ranging between 10% and 90%, and that the CO2 saturation at which the IR maxima are reached depends on the aforementioned models. Moreover, the IR are still sensitive to different CO2 saturations for a sealed CO2 reservoir covered by a clay layer. These results, which should be complemented by the analysis of the IR absolute amplitude, could lead, once confirmed on the field, to a new monitoring tool complementing existing ones.

Analysis and measurement of the modulation transfer function of harmonic shear wave induced phase encoding imaging.

Shear wave induced phase encoding (SWIPE) imaging generates ultrasound backscatter images of tissue-like elastic materials by using traveling shear waves to encode the lateral position of the scatters in the phase of the received echo. In contrast to conventional ultrasound B-scan imaging, SWIPE offers the potential advantages of image formation without beam focusing or steering from a single transducer element, lateral resolution independent of aperture size, and the potential to achieve relatively high lateral resolution with low frequency ultrasound. Here a Fourier series description of the phase modulated echo signal is developed, demonstrating that echo harmonics at multiples of the shear wave frequency reveal target k-space data at identical multiples of the shear wavenumber. Modulation transfer functions of SWIPE imaging systems are calculated for maximum shear wave acceleration and maximum shear constraints, and compared with a conventionally focused aperture. The relative signal-to-noise ratio of the SWIPE method versus a conventionally focused aperture is found through these calculations. Reconstructions of wire targets in a gelatin phantom using 1 and 3.5 MHz ultrasound and a cylindrical shear wave source are presented, generated from the fundamental and second harmonic of the shear wave modulation frequency, demonstrating weak dependence of lateral resolution with ultrasound frequency.

Analysis and measurement of the modulation transfer function of harmonic shear wave induced phase encoding imaging

B-scan imaging relies on geometric focusing of ultrasound echoes. In contrast, the method of Shear Wave Induced Phase Encoding imaging achieves lateral resolution of an elastic target by using traveling shear waves to encode the position of scatters in the phase of the received echo. A Fourier series description of the phase modulated echo signal is developed, demonstrating that echo harmonics at multiples of the shear wave frequency reveal target k-space data at identical multiples of the shear wavenumber. Modulation transfer functions (MTFs) are calculated for maximum shear wave acceleration and maximum shear constraints, and compared with a conventionally focused aperture. The relative SNR of this method versus a conventionally focused aperture is determined from these MTFs. Reconstructions of wire targets in a gelatin phantom using a cylindrical shear wave source are presented, including Images generated from the fundamental and second harmonic of the shear wave modulation frequency. Comparison of images generated at 1 and 3.5 MHz demonstrate the weak dependence of lateral resolution on ultrasound frequency with this method.

Estimation of seabed shear-wave velocity profiles using shear-wave source data

This paper estimates seabed shear-wave velocity profiles and their uncertainties using interface-wave dispersion curves extracted from data generated by a shear-wave source. The shear-wave source generated a seismic signature over a frequency range between 2 and 60 Hz and was polarized in both in-line and cross-line orientations. Low-frequency Scholte- and Love-waves were recorded. Dispersion curves of the Scholte- and Love-waves for the fundamental mode and higher-order modes are extracted by three time-frequency analysis methods. Both the vertically and horizontally polarized shear-wave velocity profiles in the sediment are estimated by the Scholte- and Love-wave dispersion curves, respectively. A Bayesian approach is utilized for the inversion. Differential evolution, a global search algorithm is applied to estimate the most-probable shear-velocity models. Marginal posterior probability profiles are computed by Metropolis-Hastings sampling. The estimated vertically and horizontally polarized shear-wave velocity profiles fit well with the core and in situ measurements.

A new electrical and mechanically detonatable shear wave source for near surface (0–30m) seismic acquisition

We present a new, impulsive, horizontal shear source capable of performing long shot profiles in a time-efficient and repeatable manner. The new shear source is ground-coupled by eight 1/2″ (1.27 cm) × 2″ (5.08 cm) steel spikes. Blank shotshells (12-gauge) used as energy sources can be either mechanically or electrically detonated. Electrical fuses have a start time repeatability of < 50 μs. This source can be operated by a single individual, and takes only ~ 10 s between shots as opposed to ~ 30 s for six stacked hammer blows. To ensure complete safety, the shotshell holder is surrounded by a protective 6″ (15.24 cm)-thick barrel, a push-and-twist-locked breach, and a safety pin. We conducted field tests at the 17th Street Canal levee breach site in New Orleans, Louisiana (30.017° N 90.121° W) and at an instrumented test borehole at Millsaps College in Jackson, Mississippi (32.325° N 93.182° W) to compare our new source and a traditional hammer impact source. The new shear source produces a broader-band of frequencies (30–100 Hz cf. 30–60 Hz). Signal generated by the new shear source has signal-to-noise ratios equivalent to ~ 3 stacked hammer blows to the hammer impact source. Ideal source signals must be broadband in frequency, have a high SNR, be consistent, and have precise start times; all traits of the new shear source.

Estimating fracture orientation from elastic‐wave propagation: An ultrasonic experimental approach

Elastic‐wave propagation in fractured and cracked media depends on the dominant spatial orientation of the discontinuities. Consequently, compressional and shear‐wave velocities can give valuable information about the orientation of the cracks. The main goal of this work is to estimate the preferential fracture orientation based on an analysis of cross‐correlated S‐wave seismograms and Thomsen parameters. For this purpose, we analyzed ultrasonic measurements of elastic (P and S) waves in a physical‐modeling experiment with an artificially anisotropic cracked model. The solid matrix of the model consisted of epoxy‐resin; small rubber strips simulate cracks with a compliant fill. The anisotropic cracked model consists of three regions, each with a different fracture orientation. We used the rotation of the S‐wave polarizations for a cross‐correlation analysis of the orientations, and P‐ and S‐wave measurements to evaluate the weak anisotropic parametersγandε.The shear and compressional wave sources had dominant frequencies of 90 kHz and 120 kHz. These frequencies correspond to long wavelengths compared to the spacing between layers, indicating a nearly effective‐media behavior. Integrating the results from cross‐correlation with anisotropic parameter analysis, we were able to estimate the fracture orientation in our anisotropic cracked physical model. Theγparameter showed good agreement with the cross‐correlation analysis and, beyond that, provided additional information about the crack orientation that cross‐correlation alone did not fully resolve. Moreover, our results show that the shear waves are much more strongly influenced by, and can thus contain more information about, crack orientation than compressional waves.

Improving arrival time identification in transient elastography

In this paper, we improve the first step in the arrival time algorithm used for shear wave speed recovery in transient elastography. In transient elastography, a shear wave is initiated at the boundary and the interior displacement of the propagating shear wave is imaged with an ultrasound ultra-fast imaging system. The first step in the arrival time algorithm finds the arrival times of the shear wave by cross correlating displacement time traces (the time history of the displacement at a single point) with a reference time trace located near the shear wave source. The second step finds the shear wave speed from the arrival times. In performing the first step, we observe that the wave pulse decorrelates as it travels through the medium, which leads to inaccurate estimates of the arrival times and ultimately to blurring and artifacts in the shear wave speed image. In particular, wave ‘spreading’ accounts for much of this decorrelation. Here we remove most of the decorrelation by allowing the reference wave pulse to spread during the cross correlation. This dramatically improves the images obtained from arrival time identification. We illustrate the improvement of this method on phantom and in vivo data obtained from the laboratory of Mathias Fink at ESPCI, Paris.

Calculation of shear stiffness in noise dominated magnetic resonance elastography data based on principal frequency estimation

Magnetic resonance elastography (MRE) is a non-invasive phase-contrast-based method for quantifying the shear stiffness of biological tissues. Synchronous application of a shear wave source and motion encoding gradient waveforms within the MRE pulse sequence enable visualization of the propagating shear wave throughout the medium under investigation. Encoded shear wave-induced displacements are then processed to calculate the local shear stiffness of each voxel. An important consideration in local shear stiffness estimates is that the algorithms employed typically calculate shear stiffness using relatively high signal-to-noise ratio (SNR) MRE images and have difficulties at an extremely low SNR. A new method of estimating shear stiffness based on the principal spatial frequency of the shear wave displacement map is presented. Finite element simulations were performed to assess the relative insensitivity of this approach to decreases in SNR. Additionally, ex vivo experiments were conducted on normal rat lungs to assess the robustness of this approach in low SNR biological tissue. Simulation and experimental results indicate that calculation of shear stiffness by the principal frequency method is less sensitive to extremely low SNR than previously reported MRE inversion methods but at the expense of loss of spatial information within the region of interest from which the principal frequency estimate is derived.