Shear Attenuation Research Articles

Shear waves and sound attenuation in underwater waveguides.

In addition to dissipation of acoustic energy in the seabed, bottom-interacting normal modes are attenuated by radiation of shear waves into soft sediments, where shear speed is small compared to the sound speed in water. The shear-wave contribution and the dissipation have distinct frequency dependencies, and their relative magnitude affects the observed frequency dependence of mode attenuation. Previous studies suggested that the shear-wave contribution to the attenuation is proportional to the cube of the small ratio of the shear and sound speeds. Here, coupling of compressional and shear waves in layered soft sediments is analyzed. Besides the well-known, third-order contribution to the attenuation due to shear-wave generation at the water-sediment interface, a stronger, first-order, contribution is found to occur due to compressional-to-shear wave conversion at interfaces within the sediment. First-order effects of weak shear on mode travel times are also identified. Stratification of the sediment density and interference of shear waves reflected within the seabed control the frequency dependence of the shear-wave contribution to sound attenuation. With the shear-wave contribution being larger than previously estimated, its effect on the experimentally measured frequency dependence of the sound dissipation may need to be re-assessed.

Constraints on the Depth, Thickness, and Strength of the G Discontinuity in the Central Pacific From S Receiver Functions

AbstractThe relative motion of the lithosphere with respect to the asthenosphere implies the existence of a boundary zone that accommodates shear between the rigid plates and flowing mantle. This shear zone is typically referred to as the lithosphere‐asthenosphere boundary (LAB). The width of this zone and the mechanisms accommodating shear across it have important implications for coupling between mantle convection and surface plate motion. Seismic observations have provided evidence for several physical mechanisms that might help enable relative plate motion, but how these mechanisms each contribute to the overall accommodation of shear remains unclear. Here we present receiver function constraints on the discontinuity structure of the oceanic upper mantle at the NoMelt site in the central Pacific, where local constraints on shear velocity, anisotropy, conductivity, and attenuation down to ∼300 km depth provide a comprehensive picture of upper mantle structure. We image a seismic discontinuity with a Vsv decrease of 4.5% or more over a 0–20 km thick gradient layer centered at a depth of ∼65 km. We associate this feature with the Gutenberg discontinuity (G), and interpret our observation of G as resulting from strain localization across a dehydration boundary based on the good agreement between the discontinuity depth and that of the dry solidus. Transitions in Vsv, azimuthal anisotropy, conductivity, and attenuation observed at roughly similar depths suggest that the G discontinuity represents a region of localized strain within a broader zone accommodating shear between the lithosphere and asthenosphere.

Seismic evidence for partial melt below tectonic plates.

The seismic low-velocity zone (LVZ) of the upper mantle is generally associated with a low-viscosity asthenosphere that has a key role in decoupling tectonic plates from the mantle1. However, the origin of the LVZ remains unclear. Some studies attribute its low seismic velocities to a small amount of partial melt of minerals in the mantle2,3, whereas others attribute them to solid-state mechanisms near the solidus4-6 or the effect of its volatile contents6. Observations of shear attenuation provide additional constraints on the origin of the LVZ7. On the basis of the interpretation of global three-dimensional shear attenuation and velocity models, here we report partial melt occurring within the LVZ. We observe that partial melting down to 150-200 kilometres beneath mid-ocean ridges, major hotspots and back-arc regions feeds the asthenosphere. A small part of this melt (less than 0.30 per cent) remains trapped within the oceanic LVZ. Melt is mostly absent under continental regions. The amount of melt increases with plate velocity, increasing substantially for plate velocities of between 3 centimetres per year and 5 centimetres per year. This finding is consistent with previous observations of mantle crystal alignment underneath tectonic plates8. Our observations suggest that by reducing viscosity9 melt facilitates plate motion and large-scale crystal alignment in the asthenosphere.

Process−microstructure−properties relationship in Al−CNTs−Al2O3 nanocomposites manufactured by hybrid powder metallurgy and microwave sintering process

Abstract Al−2CNTs−xAl2O3 nanocomposites were manufactured by a hybrid powder metallurgy and microwave sintering process. The correlation between process-induced microstructural features and the material properties including physical and mechanical properties as well as ultrasonic parameters was measured. It was found that physical properties including densification and physical dimensional changes were closely associated with the morphology and particle size of nanocomposite powders. The maximum density was obtained by extensive particle refinement at milling time longer than 8 h and Al2O3 content of 10 wt.%. Mechanical properties were controlled by Al2O3 content, dispersion of nano reinforcements and grain size. The optimum hardness and strength properties were achieved through incorporation of 10 wt.% Al2O3 and homogenous dispersion of CNTs and Al2O3 nanoparticles (NPs) at 12 h of milling which resulted in the formation of high density of dislocations and extensive grain size refinement. Also both longitudinal and shear velocities and attenuation increase linearly by increasing Al2O3 content and milling time. The variation of ultrasonic velocity and attenuation was attributed to the degree of dispersion of CNTs and Al2O3 and also less inter-particle spacing in the matrix. The larger Al2O3 content and more homogenous dispersion of CNTs and Al2O3 NPs at longer milling time exerted higher velocity and attenuation of ultrasonic wave.

Bulk, shear and scattering attenuation beneath Hawaiian Volcanos and in the oceanic crust extending to the Aloha Cabled Observatory

SUMMARYSeismic attenuation is measured from a swarm of 50 earthquakes in Kīlauea volcano in 2018, associated with caldera collapse. The traverse extends at nearly constant azimuth to the saddle between Mauna Loa and Mauna Kea, continuing to Maui beneath the distal flanks of three dormant volcanos. From Maui the traverse then extends seaward to the Aloha Cabled Observatory (ACO) on the seafloor north of O‘ahu. The effective attenuation is measured with respect to an ${\omega ^{ - 2}}$ earthquake source model. Frequency dependent ${Q_P}$ and ${Q_S}$ are derived. The initial path is shallow and uphill, the path to Maui propagates at mid-crustal depths, and the path to ACO extends through oceanic crust. The observations of ${Q_P} \le {Q_S}$ over each traverse are modelled as bulk attenuation ${Q_K}$. Several attenuation processes are observed, including ${Q_\mu }$, ${Q_K}$, $Q\sim f$, constant Q and scattering. The observation of bulk attenuation is ascribed to contrasting physical properties between basalt and water saturated vesicles. The ratio of Q values between shallow and mid-crustal propagation is used to derive an activation energy E* for the undetermined shear attenuation mechanism. A Debye relaxation peak is fit to the ${Q_S}( f )$ and ${Q_K}( f )$ observed for the mid-crustal pathway. A prior high-frequency attenuation study near Wake Island compares well with this Hawaiian Q data set, which in general shows lower values of Q than observed for Wake.

Shear attenuation and anelastic mechanisms in the central Pacific upper mantle

We determine the mantle attenuation (1/Qμ) structure beneath 70 Myr seafloors in the central Pacific. We use long-period (33-100 sec) Rayleigh waves recorded by the NoMelt array of broadband ocean-bottom seismometers. After the removal of tilt and compliance noise, we are able to measure Rayleigh wave phase and amplitude for 125 earthquakes. The compliance correction for ocean wave pressure on the seafloor is particularly important for improving signal-to-noise at periods longer than 55 sec. Attenuation and azimuthally anisotropic phase velocity in the study area are determined by approximating the wavefield as the interference of two plane waves. We find that the amplitude decay of Rayleigh waves across the NoMelt array can be adequately explained using a two-layer model: Qμ=1400 in the shallow layer, Qμ=110 in the deeper layer, and a transition depth at 70 km, although the sharpness of the transition is not well resolved by the Rayleigh wave data. Notably, Qμ observed in the NoMelt lithosphere is significantly higher than values in this area from global attenuation models. When compared with lithospheric Qμ measured at higher frequency (∼3 Hz), the frequency dependence of attenuation is very slight, revising previous interpretations. The effect of anelasticity on shear velocity (VS) is estimated from the ratio of observed velocity to the predicted anharmonic value. We use laboratory-based parameters to predict attenuation and velocity-dispersion spectra that result from the superposition of a weakly frequency dependent high-temperature background and an absorption peak. We test a large range of frequencies for the position of the absorption peak (fe) and determine, at each depth, which values of fe predict Qμ and VS that can fit the NoMelt Qμ and VS values simultaneously. We show that between depths of 60 and 80 km the seismic models require an increase in fe by at least 3-4 orders of magnitude. Under the assumption that the absorption peak is caused by elastically accommodated grain-boundary sliding, this increase in fe reflects a decrease in grain-boundary viscosity of 3-4 orders of magnitude. A likely explanation is an increase in the water content of the mantle, with the base of the dehydrated lid located at ∼70-km depth.

High Bulk and Shear Attenuation Due to Partial Melt in the Tonga‐Lau Back‐arc Mantle

AbstractSeismic attenuation measures energy loss during seismic wave propagation and quantifies the relaxation of rocks' elastic moduli. Abundant seismic studies have observed shear attenuation, but few have quantified bulk attenuation (bulk modulus relaxation), and these studies controversially locate finite bulk attenuation in different parts of the Earth, from the asthenosphere to the inner core. Here we present conclusive evidence localizing bulk attenuation to a specific region of the uppermost mantle. By analyzing amplitude spectral decay of P and S waves from Tonga earthquakes recorded at local seismic stations, we observe unusually low QP/QS ratios (<1.5) in the Tonga‐Lau mantle wedge. All seismic raypaths with significant path‐average bulk attenuation (Qκ−1 > 0.01 or Qκ < 100) are confined to the region immediately beneath the Lau back‐arc spreading centers west of the Tonga Arc. Tomography results show that the highest bulk attenuation (Qκ−1 = 0.037 ± 0.008 or Qκ = 27.0 ± 0.2) is about 75% of the in situ shear attenuation. The observed high bulk attenuation anomalies coincide with an inferred zone of partial melting, suggesting that the causative mechanism involves either infinitesimal movement of melt through pores or changes in melt fraction in response to seismic waves.

Azimuthal Attenuation Elastic Impedance Inversion for Fluid and Fracture Characterization Based on Modified Linear-Slip Theory

The seismic attenuation should be considered while accounting for the effect of anisotropy on the seismic wave propagating through a saturated fractured porous medium. Based on the modified linear-slip theory and anisotropic Gassmann’s equation, we derive an analytical expression for a linearized PP-wave reflection coefficient and an azimuthal attenuation elastic impedance (AAEI) equation in terms of fluid/porosity term, shear modulus, density, dry normal and tangential fracture weaknesses, and compressional (P-wave) and shear (S-wave) attenuation parameters in a weak-attenuation isotropic background rock containing one single set of vertical aligned fractures. We then propose an AAEI inversion method to characterize the characteristics of fluids and fractures using two kinds of constrained regularizations in such a fractured porous medium. The proposed approach is finally confirmed by both the synthetic and real data sets acquired over a saturated fractured porous reservoir.

Electromagnetic wave propagation based upon spectral-element methodology in dispersive and attenuating media

SUMMARYWe build on mathematical equivalences between Maxwell’s wave equations for an electromagnetic medium and elastic seismic wave equations. This allows us to readily model Maxwell’s wave propagation in the spectral-element codes SPECFEM2D and SPECFEM3D, written for acoustic, viscoelastic and poroelastic seismic wave propagation, providing the ability to handle complex geometries, inherent to finite-element methods and retaining the strength of exponential convergence and accuracy due to the use of high-degree polynomials to interpolate field functions on the elements, characteristic to spectral-element methods (SEMs). Attenuation and dispersion processes related to the frequency dependence of dielectric permittivity and conductivity are also included using a Zener model, similar to shear attenuation in viscoelastic media or viscous diffusion in poroelastic media, and a Kelvin–Voigt model, respectively. Ability to account for anisotropic media is also discussed. Here, we limit ourselves to certain dielectric permittivity tensor geometries, in order to conserve a diagonal mass matrix after discretization of the system of equations. Doing so, simulation of Maxwell’s wave equations in the radar frequency range based on SEM can be solved using explicit time integration schemes well suited for parallel computation. We validate our formulation with analytical solutions. In 2-D, our implementation allows for the modelling of both a transverse magnetic (TM) mode, suitable for surface based reflection ground penetration radar type of applications, and a transverse electric (TE) mode more suitable for crosshole and vertical radar profiling setups. Two 2-D examples are designed to demonstrated the use of the TM and TE modes. A 3-D example is also presented, which allows for the full TEM solution, different antenna orientations, and out-of-plane variations in material properties.

Determination of formation shear attenuation from dipole sonic log data

ABSTRACT Formation S-wave attenuation, when combined with compressional attenuation, serves as a potential hydrocarbon indicator for seismic reservoir characterization. Sonic flexural wave measurements provide a direct means for obtaining the in situ S-wave attenuation at log scale. The key characteristic of the flexural wave is that it propagates at the formation shear slowness and experiences shear attenuation at low frequency. However, in a fast formation, the dipole log consists of refracted P- and S-waves in addition to the flexural wave. The refracted P-wave arrives early and can be removed from the dipole waveforms through time windowing. However, the refracted S-wave, which is often embedded in the flexural wave packet, is difficult to separate from the dipole waveforms. The additional energy loss associated with the refracted S-wave results in the estimated dipole attenuation being higher than the shear attenuation at low frequency. To address this issue, we have developed a new method for accurately determining the formation shear attenuation from the dipole sonic log data. The method uses a multifrequency inversion of the frequency-dependent flexural wave attenuation based on energy partitioning. We first developed our method using synthetic data. Application to field data results in a shear attenuation log that is consistent with lithologic interpretation of other available logs.

Low‐Frequency Measurements of Seismic Moduli and Attenuation in Antigorite Serpentinite

AbstractLaboratory measurements of seismic moduli and attenuation in antigorite serpentinite at a confining pressure of 200 MPa and temperatures up to 550 °C provide new results relevant to the interpretation of geophysical data in subduction zones. A polycrystalline antigorite specimen was tested via forced oscillations at small strain amplitudes and seismic frequencies (millihertz to hertz). The shear modulus has a temperature sensitivity, ∂G/∂T, averaging −0.017 GPa/K. Increasing temperature above 500 °C results in more intensive shear attenuation ( ) and associated modulus dispersion, with increasing monotonically with increasing oscillation period and temperature. This “background” relaxation is adequately captured by a Burgers model for viscoelasticity and possibly results from intergranular mechanisms. Attenuation is higher in antigorite ( at 550 °C and 0.01 Hz) than in olivine ( below 800 °C), but such contrast does not appear to be strong enough to allow robust identification of antigorite from seismic models of attenuation only.

Scattering and intrinsic attenuation as a potential tool for studying of a fractured reservoir

Intrinsic attenuation is mainly caused by the frictional movement induced by seismic waves during their passage between fluids contained in subsurface pores and solid grains. In contrast, scattering attenuation is due to small reflections caused by subsurface heterogeneities. Since porosity and fractures are important sources of heterogeneity and fluids, scattering and intrinsic attenuation are suitable seismic attributes for investigating porous and fractured subsurface zones, such as oil and gas reservoirs. In the present study, we accurately estimated scattering and intrinsic attenuation from zero-offset vertical seismic profiling (VSP) and sonic data acquired from three wells that cross a reservoir zone of an oilfield located in Abu Dhabi in the United Arab Emirates. In addition, we properly separated scattering and intrinsic attenuation. The attenuation profiles show high variation with depth. Furthermore, the scattering is frequency dependent and has a significant contribution to the total attenuation. This is due to the high heterogeneous property of carbonate rocks, which dominate the lithology of the reservoir zone. This means that the variation of attenuation can be used as an indicator of the heterogeneity degree of reservoir zone. The VSP and sonic intrinsic attenuations exhibit high anomalies in oil-rich zones, and the ratio of the compressional sonic attenuation to the shear attenuation exhibits a high anomaly in gas-rich zones, but not in oil-rich zones, because the presence of oil influences the compressional and shears attenuations in a similar fashion. However, the presence of gas attenuates compressional waves much more than the shear waves. Therefore, can be used to distinguish oil- and gas-rich zones. The highly fractured reservoir units display negative VSP intrinsic attenuation anomalies and strong scattering, which reveals a strong interference phenomenon. This phenomenon leads to an increase in amplitude of the downgoing wave versus depth, which results in negative attenuation. Hence, strong negative intrinsic attenuation accompanied by strong scattering can be an indicator of a highly fractured zone. The VSP and sonic intrinsic attenuations in such zones have a large discrepancy, which might be due to the squirt flow mechanism due to the inter-crack fluid flow due to the compressional stress induced by seismic waves on the fractures. This mechanism attenuates the waves propagating at low frequencies less, because the fluid pressure has sufficient time to reach equilibrium, which is not the case at high frequencies. This explains why the VSP intrinsic attenuation is much smaller than the sonic attenuation in highly fractured zones. As such, a large discrepancy between VSP and sonic intrinsic attenuations also indicates a highly fractured reservoir.

Ultrasound Shear Wave Elastography as a Measure of Porcine Hepatic Disease in Right Heart Dysfunction: A Pilot Study

Patients with congenital heart disease with a pressure-overloaded right ventricle can develop liver disease and would benefit from non-invasive diagnostic modalities such as ultrasound shear wave elastography (US SWE). We sought to investigate the ability of US SWE to measure dynamic changes in liver stiffness with an acute fluid bolus in an animal model. Three piglets underwent surgical intervention to create a pressure-overloaded right ventricle and, 12 wk later, underwent US SWE, both pre- and post-intravenous infusion of a saline bolus. Ultrasound measures of shear modulus, velocity and attenuation were taken to characterize hepatic mechanical properties. Liver stiffness exhibited a dynamic component that increased after fluid bolus, although not reaching statistical significance with our small sample size, and these changes were greater in more diseased livers. US SWE may provide a promising non-invasive method for assessing dynamic changes in hydration status and degree of liver disease.

Shear attenuation beneath the Juan de Fuca plate: Implications for mantle flow and dehydration

At mid-ocean-ridge spreading centers, the separation of lithospheric plates induces upwelling and pressure-release melting in the upper mantle. Many questions remain about the associated flow pattern, melt distribution, and the interaction of spreading centers with hotspots. Based on the propagation of Rayleigh waves across arrays of ocean-bottom seismometers, we present shear wave attenuation and velocity models in the vicinity of the Juan de Fuca plate with the best resolution to date of any spreading center. There is strong attenuation centered at depths of 70–80 km, just below the expected dry solidus. The top of the attenuating region is somewhat deeper than predicted for the thermal effects of passive mantle upwelling beneath the spreading center. The shear velocity structure shows the lowest velocities west of the spreading center, particularly near Axial Seamount and high velocities east of the axis extending to a greater depth than predicted by the passive flow model. Together, these observations support a model in which buoyant upwelling and melt extraction west of the spreading center first depletes and dehydrates the mantle above the dry solidus and then the associated downwelling carries depleted, melt-free, residual mantle downward beneath the Juan de Fuca plate. The shear velocities and attenuation can be well matched with a model in which the dominant changes in the physical properties occur just before the onset of melting.

Characterization of Small Renal Tumors With Magnetic Resonance Elastography: A Feasibility Study.

The aim of this study was to explore the feasibility of magnetic resonance elastography (MRE) for characterizing indeterminate small renal tumors (SRTs) as part of a multiparametric magnetic resonance (MR) imaging protocol. After institutional review board approval and informed consent were obtained, 21 prospective adults (15 men; median age, 55 years; age range, 25-72 years) with SRT were enrolled. Tumors (2-5 cm Ø) were imaged using 3-directional, gradient echo MRE. Viscoelastic parametric maps (shear wave velocity [c] and attenuation [α]) were analyzed by 2 independent radiologists. Interobserver agreement (Bland-Altman statistics and intraclass correlation coefficients) was assessed. Anatomical T2-weighted, dynamic contrast-enhanced (DCE) and diffusion sequences completed the acquisition protocol. Imaging parameters were compared between groups (Mann-Whitney U test). Quality of MRE was good in 18 cases (mean nonlinearity <50%), including 1 papillary renal cell carcinoma and 1 metanephric adenoma. A cohort of 5 oncocytomas and 11 clear-cell renal cell carcinomas (ccRCCs) was analyzed for statistical differences. The MRE viscoelastic parameters were the strongest imaging discriminators: oncocytomas displayed significantly lower shear velocity c (median, 0.77 m/s; interquartile range [IQR], 0.76-0.79) (P = 0.007) and higher shear attenuation α (median, 0.087 mm; IQR, 0.082-0.087) (P = 0.008) than ccRCC (medians, 0.92 m/s and 0.066 mm; IQR, 0.84-0.97 and 0.054-0.074, respectively). T2 signal intensity ratio (tumor/renal cortex) was lower in oncocytomas (P = 0.02). The DCE and diffusion MR parameters overlapped substantially (P ≥ 0.1). Oncocytomas displayed a consistent MRE viscoelastic profile, corresponding to data point clustering in a bidimensional scatter plot. Values for MRE intraclass correlation coefficient were 0.982 for c and 0.984 for α, indicating excellent interobserver agreement. Magnetic resonance elastography is feasible for SRT characterization; MRE viscoelastic parameters were stronger discriminators between oncocytoma and ccRCC than anatomical, DCE and diffusion MR imaging parameters.

Observation and modeling of acoustic scattering from a rubber spherical shell.

Acoustic backscattering from a rubber spherical shell in water is observed to contain a delayed enhancement, demonstrated to be associated with a waveguide path along the shell. This path is somewhat analogous to that of the Lamb wave observed on metallic shells. Rubber is a unique material because of its subsonic sound speed relative to water, and because shear coupling is often small enough to be neglected in typical models, making it fluid-like. This makes rubber a material of interest for coating and cloaking underwater devices and vehicles. Both fluid and elastic rubber partial wave series models are tested, using experimentally measured longitudinal and shear speeds, attenuation, and rubber density. A finite element model for the shell is also developed. Comparison of the models and experiments highlights the importance of the waveguide path to the overall scattering. Estimates for the group and phase velocities of the lowest order propagating mode in the shell are determined through waveguide normal mode analysis and Sommerfeld-Watson theory, and are shown to give good agreement with experiments in predicting the time of arrival of the waveguide path.

The coherent shear wave in suspensions

We consider a disordered suspension of spherical silica particles in water. For a particle size of a few hundred nanometres and concentration (volume fraction) around 0.15 to 0.2, experiments conducted in the MHz range have shown that the non ideal nature of water must be taken into account for the "longitudinal" coherent wave attenuation to be understood, because of wave conversions, from longitudinal to shear and then back to longitudinal, occurring at each pair of scattering events. We are interested here in the properties of the "shear" coherent wave that are given by the expansion of its squared wavenumber, around that in the absence of particles, in powers of the concentration. At 1 MHz and a particle radius of 0.05 μm, we show that convergence of the modal series involved in that expansion may be reached after three terms: we use ten terms subsequently. We study the evolution of both the effective shear velocity and attenuation with concentration, as well as that of the effective shear viscosity deduced therefrom.

Impact of Acoustic Radiation Force Excitation Geometry on Shear Wave Dispersion and Attenuation Estimates

Shear wave elasticity imaging (SWEI) characterizes the mechanical properties of human tissues to differentiate healthy from diseased tissue. Commercial scanners tend to reconstruct shear wave speeds for a region of interest using time-of-flight methods reporting a single shear wave speed (or elastic modulus) to the end user under the assumptions that tissue is elastic and shear wave speeds are not dependent on the frequency content of the shear waves. Human tissues, however, are known to be viscoelastic, resulting in dispersion and attenuation. Shear wave spectroscopy and spectral methods have been previously reported in the literature to quantify shear wave dispersion and attenuation, commonly making an assumption that the acoustic radiation force excitation acts as a cylindrical source with a known geometric shear wave amplitude decay. This work quantifies the bias in shear dispersion and attenuation estimates associated with making this cylindrical wave assumption when applied to shear wave sources with finite depth extents, as commonly occurs with realistic focal geometries, in elastic and viscoelastic media. Bias is quantified using analytically derived shear wave data and shear wave data generated using finite-element method models. Shear wave dispersion and attenuation bias (up to 15% for dispersion and 41% for attenuation) is greater for more tightly focused acoustic radiation force sources with smaller depths of field relative to their lateral extent (height-to-width ratios <16). Dispersion and attenuation errors associated with assuming a cylindrical geometric shear wave decay in SWEI can be appreciable and should be considered when analyzing the viscoelastic properties of tissues with acoustic radiation force source distributions with limited depths of field.

Inferring global upper-mantle shear attenuation structure by waveform tomography using the spectral element method

Inferring global upper-mantle shear attenuation structure by waveform tomography using the spectral element method

Global seismic attenuation imaging using full-waveform inversion: a comparative assessment of different choices of misfit functionals

Author(s): Karaoglu, H; Romanowicz, B | Abstract: We present the results of synthetic tests that aim at evaluating the relative performance of three different definitions of misfit functionals in the context of 3-D imaging of shear wave attenuation in the earth's upper mantle at the global scale, using long-period full-waveform data. The synthetic tests are conducted with simple hypothetical upper-mantle models that contain Qμ anomalies centred at different depths and locations, with or without additional seismic velocity anomalies. To build synthetic waveform data sets, we performed simulations of 50 events in the hypothetical (target) models, using the spectral element method, filtered in the period range 60-400 s. The selected events are chosen among 273 events used in the development of radially anisotropic model SEMUCB-WM1 and recorded at 495 stations worldwide. The synthetic Z-component waveforms correspond to paths and time intervals (fundamental mode and overtone Rayleigh waves) that exist in the real waveform data set. The inversions for shear attenuation structure are carried out using a Gauss-Newton optimization scheme in which the gradient and Hessian are computed using normal mode perturbation theory. The three different misfit functionals considered are based on time domain waveform (WF) and waveform envelope (E-WF) differences, as well as spectral amplitude ratios (SA), between observed and predicted waveforms.We evaluate the performance of the three misfit functional definitions in the presence of seismic noise and unresolved S-wave velocity heterogeneity and discuss the relative importance of physical dispersion effects due to 3-D Qμ structure. We observed that the performance of WF is poorer than the other two misfit functionals in recovering attenuation structure, unless anelastic dispersion effects are taken into account in the calculation of partial derivatives. WF also turns out to be more sensitive to seismic noise than E-WF and SA. Overall, SA performs best for attenuation imaging. Our tests show that it is important to account for 3-D elastic effects (focusing) before inverting for Qμ. Additionally, we show that including high signal-to-noise ratio overtone wave packets is necessary to resolve Qμ structure at depths greater than 250 km.