Multiscale Inversion Research Articles

WUS256: An Adjoint Waveform Tomography Model of the Crust and Upper Mantle of the Western United States for Improved Waveform Simulations

AbstractWe report a new model (WUS256) of radially anisotropic seismic wavespeeds of the crust and upper mantle of the western United States (WUS) obtained from adjoint waveform tomography for the purpose of improving synthetic waveform fits to observed data. WUS256 is based on inversion of over 94,000 waveforms from 72 earthquakes recorded by nearly 3,400 stations. We started with the SPiRaL global model (Simmons et al., 2021, https://doi.org/10.1093/gji/ggab277) and waveforms in the period band of 50–120 s. We followed a conservative multiscale inversion approach with eight stages and 256 total inversion iterations which enabled monotonic misfit reduction to 20‐s minimum‐period waves. WUS256 relied on time‐frequency (TF) phase misfits and a trust region limited memory Broyden–Fletcher–Goldfarb–Shanno (L‐BFGS) optimization. Hessian‐vector products were used to qualitatively assess model resolution. Results indicate that WUS256 has good coverage of the continental regions to depths of about 150 km and is able to resolve features on lateral scales of about 200 km. We quantify waveform fits by the reduction in TF and normalized amplitude difference misfits between WUS256 and the SPiRaL starting model. WUS256 significantly improves waveform fits with misfit reduction 64% for both inversion and validation data sets compared to the SPiRaL starting model and shows even better fits compared to other models. Waveform fits illustrate that WUS256 reproduces body‐waves, fundamental mode surface waves as well as late arriving dispersed and/or scattered short period surface waves. The improvement in waveform fit indicates that WUS256 can be used to reproduce path effects on regional complete waveforms and moment tensor inversions.

Multi-scale seismic envelope inversion method based on sparse representation theory

Combining seismic data with a constrained model can obtain a high-resolution inversion result. However, it is very difficult to obtain an accurate low-frequency model because of the lack of wells in the offshore exploration area. We propose a multi-scale seismic envelope inversion method based on sparse representation to solve the problem of seismic inversion in offshore well-less areas. First, we demodulate the envelope of the seismic signal based on signal modulation theory and take it as the low-frequency component for inversion. Then, decompose the seismic signal based on MPSTFT (Short-Time Fourier Transform based on Matching Pursuit algorithm) method to provide high-resolution components of intermediate-frequency and high-frequency. Next, we take the linear impedance model as the initial model and update the inversion results by multi-scale inversion based on Bayesian inversion theory. Finally, we use the synthetic data to demonstrate the effectiveness of the proposed method and apply it to real seismic data. Comparing inversion results, the result of the proposed is more accurate and possesses a higher resolution. The results show that the proposed method has good adaptability to solve the problem of offshore well-less area inversion with a high-resolution inversion result.

Quantitative ultrasound brain imaging with multiscale deconvolutional waveform inversion

High-resolution images of human brain are critical for monitoring the neurological conditions in a portable and safe manner. Sound speed mapping of brain tissues provides unique information for such a purpose. In addition, it is particularly important for building digital human acoustic models, which form a reference for future ultrasound research. Conventional ultrasound modalities can hardly image the human brain at high spatial resolution inside the skull due to the strong impedance contrast between hard tissue and soft tissue. We carry out numerical experiments to demonstrate that the time-domain waveform inversion technique, originating from the geophysics community, is promising to deliver quantitative images of human brains within the skull at a sub-millimeter level by using ultra-sound signals. The successful implementation of such an approach to brain imaging requires the following items: signals of sub-megahertz frequencies transmitting across the inside of skull, an accurate numerical wave equation solver simulating the wave propagation, and well-designed inversion schemes to reconstruct the physical parameters of targeted model based on the optimization theory. Here we propose an innovative modality of multiscale deconvolutional waveform inversion that improves ultrasound imaging resolution, by evaluating the similarity between synthetic data and observed data through using limited length Wiener filter. We implement the proposed approach to iteratively update the parametric models of the human brain. The quantitative imaging method paves the way for building the accurate acoustic brain model to diagnose associated diseases, in a potentially more portable, more dynamic and safer way than magnetic resonance imaging and x-ray computed tomography.

Multiscale Full-Waveform Inversion with Land Seismic Field Data: A Case Study from the Jizhong Depression, Middle Eastern China

The Jizhong depression contains several geothermal reservoirs that are characterized by localized low-velocity anomalies. In this article, full-waveform inversion (FWI) is used to characterize these anomalies and determine their extent. This is a challenging problem because the reservoirs are quite small and the available data have usable frequencies only down to 5 Hz. An accurate-enough starting model is carefully built by using an iterative travel time tomography method combined with a cycle-skipping assessment method to begin the inversion at 5 Hz. A multiscale Laplace–Fourier-domain FWI with a layer-stripping approach is implemented on the starting model by gradually increasing the maximum offset. The result of overlapping the recovered velocity model on the migrated seismic profile shows a good correlation between the two results. The recovered model is assessed by ray tracing, synthetic seismogram modeling, checkerboard testing and comparisons with nearby borehole data. These tests indicate that low-velocity anomalies down to a size of 0.3 km × 0.3 km at a maximum depth of 2 km can be recovered. Combined with the well log data, the resulting velocity model allows us to delineate two potential geothermal resources, one of which was previously unknown.

Ambient noise tomography of Misti volcano, Peru

To better understand the recent internal structure of Misti volcano, we determined a 3D S-wave velocity model applying Ambient Noise Tomography (ANT). We used data from 23 broadband and short-period seismic stations temporarily installed at Misti volcano between March and December 2011. This dataset allowed us to obtain empirical Green's functions by cross-correlating seismic ambient noise signals. Then, we retrieved 104 dispersion curves using the frequency-time analysis (FTAN) and, through a non-linear multiscale inversion, we obtained nine 2-D Rayleigh waves group velocity maps for periods in the range 0.7 s - 2 s. Finally, we carried out the depth inversion through a Bayesian transdimensional inversion to obtain a 3-D S-wave velocity model down to 3 km depth. Our study highlights five relevant seismic velocity anomalies. We observed the presence of three high-velocity zones located in the west-northwest, southwest and southeast parts of the crater, that could be related to intrusive bodies possibly associated with the formation of Misti volcano. We also observed two low-velocity anomalies in the volcano's western and central parts, which coincide with previous studies' findings and are related to fractured and weakened materials associated with the external caldera collapse and recent eruption episodes.

Numerical Verification of Full Waveform Inversion for the Chang’E-5 Lunar Regolith Penetrating Array Radar

The lunar regolith penetrating array radar (LRPR) carried by Chang’E-5 (CE-5) has explored the subsurface regolith structure of the moon and guided the drill sampling procedures. To evaluate LRPR performance in subsurface imaging and physical-parameter estimation, we apply multiscale full-waveform inversion (FWI) with total variation (TV) regularization to the synthetic CE-5 LRPR data. The time-domain multiscale inversion strategy gives a low-frequency update for the deep region and increases the frequency range for updating the shallow area. The TV regularization reduces the image noise and improves the inversion accuracy of local structures. To mimic the actual scenario, we use an LRPR source wavelet obtained from the LRPR instrument prototype for our FWI test. The LRPR source wavelets include the effect of the antenna radiation patterns and signal scattering from the metallic lander. We test the proposed FWI scheme on two heterogeneous models of the lunar regolith and demonstrate that the scheme effectively reduces the signal scattering from the metallic lander and provides a reliable way to image the lunar regolith structures. These images can be used to estimate the regolith physical parameters.

Subsurface Elastic Parameter Reconstruction Based on Seismic Data From the High-Speed Trains Using Full Waveform Inversion

In this study, we attempt to use the high-speed train (HST)-induced seismic data for subsurface elastic parameter reconstruction by the full waveform inversion (FWI) method. The HSTs provide a new kind of seismic source as the superposition of a series of moving subsources. We consider the situation of HST running on the viaduct and use a finite difference method to simulate the seismic wave excitation. The result shows that the HST-induced seismic data are highly complex in the time domain but appear as a series of discrete peaks in the frequency domain. Elastic FWI is used to retrieve the P- and S-wave velocities of the subsurface based on this new kind of seismic data. The alternative iteration strategy and multiscale inversion are used to improve the inversion results. Numerical examples with the Marmousi2 model show the feasibility and the great potential of using this new kind of seismic data in seismic imaging.

Elastic Full Waveform Inversion Based on Full-Band Seismic Data Reconstructed by Dual Deconvolution

Affected by the low-frequency seismic data missing and multiple parameters coupling, elastic full waveform inversion is easy to fall into local minima. This paper attempts to solve the local minima problem from two aspects: low-frequency seismic data reconstruction and wave mode decomposition. First, by introducing the envelope into sparse constrained deconvolution, an envelope-based sparse constrained deconvolution method is proposed to overcome the problem caused by the phase shift and side lobes. However, the resolution of the envelope is insufficient to identify overlapping seismic events, which are generated by velocity models rich in thin layers. Therefore, sparse constrained deconvolution and envelope-based sparse constrained deconvolution are combined, and a dual deconvolution method is proposed: sparse constrained deconvolution is used to improve the resolution of the original seismic data, then envelope-based sparse constrained deconvolution is used to reconstruct high-precision reflection sequence. Convolve the reconstructed reflection sequence with the full-band source wavelet to obtain the full-band seismic data. Secondly, for the multi-parameter coupling problem, we use wave mode decomposition to obtain separated P- and S-wave. Finally, a multi-scale elastic full waveform inversion method based on dual deconvolution and wave mode decomposition is proposed. Numerical experiment results demonstrate the algorithm proposed in the article.

3D multi-scale resistivity inversion method applied in the tunnel face to borehole observations for tunnel-ahead prospecting

Many adverse geological structures, such as karst caves and faults, may exist in front of the tunnel face. If adverse geological structures ahead of the tunnel face cannot be detected clearly, geological hazards (i.e., the inrush of clay and water) may occur during excavation. In this study, a new ahead prospecting scheme was proposed to detect adverse geological structures during tunnel construction using probe holes. First, a new array was proposed: the potential electrodes were placed at the tunnel face, and the current electrodes were placed in the hole. The potential data were collected and used for inversion. Furthermore, a 3D resistivity multi-scale inversion method was proposed to locate and describe boundaries of geological structures with high accuracy. In this method, the 3D convolutional wavelet transform is used to extract wavelet parameter information from the resistivity model. On this basis, the inverted solution space is transformed from the spatial domain to the wavelet domain. The solution in the wavelet domain can be obtained using the inversion equation. Then, the solution in the spatial domain can be obtained from the wavelet domain using the 3D deconvolution transform. Finally, the effectiveness of the new ahead prospecting scheme was verified by numerical inversion tests. Furthermore, this paper describes the successful application of the new scheme to detect water-bearing structures in tunnel of the project “transfer water from Hongyan river to Shitou river”.

Multiscale phase inversion for vertical transverse isotropic media

ABSTRACTInanisotropy full waveform inversion, the pseudo‐acoustic approximation is widely used to reduce the computation cost. However, artefacts and inaccurate predictions of amplitudes by the pseudo‐acoustic approximation often result in slow convergence in the full waveform inversion iterations and inaccurate tomograms. To solve this problem, multiscale phase inversion methodology is extended to vertical transverse isotropic media. In multiscale phase inversion, the amplitude spectra of the predicted data are replaced by those of the recorded data to mitigate the amplitude mismatch problem. Moreover, multiscale phase inversion tends to avoid the local minimum problem of full waveform inversion by temporally integrating the traces several times. Numerical tests on synthetic data and field data demonstrate the superiority of this method compared to conventional multiscale full waveform inversion for vertical transverse isotropic media.

Time-lapse full waveform inversion based on curvelet transform: Case study of CO2 storage monitoring

Full waveform inversion (FWI) has high accuracy in predicting reservoir elastic parameters. Prediction of changes in reservoir elastic parameters is an effective method for CO2 storage monitoring. Therefore, FWI is of great significance in CO2 storage monitoring, however, it relies on low-frequency information and data quality and its use incurs substantial computational costs. To alleviate this problem, a multi-scale time-lapse inversion method based on the curvelet transform was proposed. Using the high sparsity of the curvelet transform, the original shot gather data can be separated into multiple scales. A multi-scale inversion process based on the curvelet transform was introduced, and a coarse to fine scale inversion was conducted. According to the multi-scale inversion strategy, the P- and S-wave velocities and densities of the reservoirs in multiple periods were obtained. The test results of Marmousi II and the manual model show that the inversion method based on the curvelet transform exhibits high accuracy in predicting reservoir elastic parameters and can clearly determine the local changes in the reservoir. The calculation time shows that the multi-scale inversion based on the curvelet transform does not reduce the calculation efficiency. In summary, the time-lapse full waveform inversion method based on the curvelet transform is highly accurate, and is therefore promisingly effective for CO2 storage monitoring.

Imaging the internal structure of trunks via multiscale phase inversion of ground-penetrating radar data

Ground-penetrating radar (GPR) is a geophysical technique widely used in near-surface noninvasive detecting. It has the ability to obtain a high-resolution internal structure of living tree trunks. Full-waveform inversion (FWI) has been widely used to reconstruct the dielectric constant and conductivity distribution for crosswell applications. However, in some cases, the amplitude information is not reliable due to the antenna coupling, radiation pattern, and other effects. We have developed a multiscale phase inversion (MPI) method, which largely matches the phase information by normalizing the magnitude spectrum; in addition, a natural multiscale approach by integrating the input data with different times is implemented to partly mitigate the local minimal problem. Two synthetic GPR data sets generated from a healthy oak tree trunk and from a decayed trunk are tested by MPI and FWI. A field GPR data set consisting of 30 common-shot GPR data is acquired on a standing white oak tree ( Quercus alba); the MPI and FWI methods are used to reconstruct the dielectric constant distribution of the tree cross section. Results indicate that MPI has more tolerance to the starting model, noise level, and source wavelet. It can provide a more accurate image of the dielectric constant distribution compared to the conventional FWI.

Far-field biogenic and anthropogenic emissions as a dominant source of variability in local urban carbon budgets: A global high-resolution model study with implications for satellite remote sensing

With the launch of the Observing Carbon Observatories (OCO-2 and OCO-3), we have entered a new era of greenhouse gas (GHG) data collection where sub-city scale data can be collected at varying times across the entire globe. An increasing focus on quantifying urban emissions of GHGs from policy makers has begun to spur new research into how best to use this unique and very high resolution data set. While, historically, this line of research has been the domain of limited domain mesoscale and regional models, an increasing understanding and respect for boundary inflow uncertainty and bias has led people to search for an alternative modeling framework that both characterizes high frequency variability of CO2 in space and time as well as honor mass conservation requirements globally and be seamless with respect to boundaries. To monitor local anthropogenic emissions from space, the influence of atmospheric signals originating from outside the local area of interest needs to be quantified. In our first step towards building a comprehensive multi-scale CO2 inversion system, we use free running simulations of the Ocean Land Atmosphere Model (OLAM), a variable-resolution general circulation model, to explore the signal-to-noise statistics of anthropogenic urban emissions of CO2 versus the background inflow for approximately 40 of the largest cities across the globe. We show that signal-to-noise levels are much better in winter time than summer but also that the winter biological inflow is far from negligible, suggesting that the commonly held assumption that biology can be ignored in winter time urban emission estimates is probably incorrect. Simulated pressure-weighted column average CO2 (XCO2) is also used to evaluate the ability of fixed location XCO2 measurements to provide background inflow estimates. Results show why Los Angeles, a heavily instrumented and studied urban center, is likely one of the easiest cities to observe globally from space, despite its relatively complex meteorology. Lastly, we discuss challenges and possible research paths forward to continue to advance the notion of multi-scale global CO2 flux inversion systems capable of simultaneously optimizing local urban emissions and large-scale CO2 transport patterns.

Advanced three-dimensional electromagnetic modelling using a nested integral equation approach

SUMMARY Most of the existing 3-D electromagnetic (EM) modelling solvers based on the integral equation (IE) method exploit fast Fourier transform (FFT) to accelerate the matrix–vector multiplications. This in turn requires a laterally uniform discretization of the modelling domain. However, there is often a need for multiscale modelling and inversion, for instance, to properly account for the effects of non-uniform distant structures and, at the same time, to accurately model the effects from local anomalies. In such scenarios, the usage of laterally uniform grids leads to excessive computational loads, in terms of both memory and time. To alleviate this problem, we developed an efficient 3-D EM modelling tool based on a multinested IE approach. Within this approach, the IE modelling is first performed at a large domain and on a (laterally uniform) coarse grid, and then the results are refined in the region of interest by performing modelling at a smaller domain and on a (laterally uniform) denser grid. At the latter stage, the modelling results obtained at the previous stage are exploited. The lateral uniformity of the grids at each stage allows us to keep using the FFT for the acceleration of matrix–vector multiplications. An important novelty of the paper is the development of a ‘rim domain’ concept that further improves the performance of the multinested IE approach. We verify the developed tool on both idealized and realistic 3-D conductivity models, and demonstrate its efficiency and accuracy.

Multi-scale phase waveform inversion method of on-ground GPR data

Full waveform inversion of ground penetrating radar (GPR) based on Maxwell’s equations can invert the permittivity and conductivity of the underground medium, and achieve quantitative interpretation of the target formation. Here, we present a GPR waveform inversion method based on the phase misfit function, and inverts the phase information in the GPR data. By analyzing the characteristics of phase transformation, the misfit function of PWI is given. The gradient is constructed by the convolution of the forward and reverse fields, and its gradient formula is derived. When the transmitting source and receiver of GPR are arranged on the ground, the waveform inversion can only use the scattered field to obtain the effective information of the underground medium, and the inversion will face a strong indetermination. The inversion is more dependent on the initial model than the cross-hole GPR waveform inversion, but non-destructive detection often lacks prior information. In order to solve this problem, this paper makes use of the characteristics of integral operation and formulates a multi-scale inversion strategy. In the iterative process of inversion, high integration times are preferentially used to restore long wavelength information. This can reduce the dependence of the waveform inversion on the initial model as much as possible, implement the waveform inversion method for on-ground GPR data, and verify it with two sets of synthetic data.

Mapping complex reservoir targets by electromagnetic multi-attributes

In development of oil and gas exploration, complex reservoirs have become a key problem for increasing production capacity. It is of great significance to develop novel technologies for reservoir prediction and evaluation. Non-seismic methods such as time-frequency electromagnetics and well-ground electromagnetics have been applied to the study of complex reservoirs, oil and gas detection methods of electromagnetic properties based on the analysis of dispersion characteristics and a method of oil and gas target identification based on complex resistivity equivalent models have been proposed and the method of inversion of electromagnetic properties of complex reservoirs using the well-ground multi-scale sequential constraint inversion method, etc., introduces the actual profiles applied to the development of exploration of igneous rocks and complicated fault-block lithological reservoirs. It provides an effective method for oil and gas detection of knew hydrocarbon traps in complex targets of oil and gas.

A Multi-scale Inversion Method Based on Convolutional Wavelet Transform Applied in Cross-Hole Resistivity Electrical Tomography

With the increasing demand for fine exploration, there is also a growing demand on the use of the cross-hole electrical resistivity tomography (ERT). However, the boundaries of geological bodies cannot be accurately described when traditional smooth constraint method was adopted. To solve this problem, we studied a multi-scale inversion method based on convolution wavelet transform. The finite element method is used in the modeling process. The imaging effects of numerical simulation are discussed, such as a single rectangular target, two rectangular targets, Irregular targets, and layered models. The effectiveness of multi-scale methods in cross-hole ERT has been revealed in this work.

Rock Fracture Monitoring Based on High-Precision Microseismic Event Location Using 3D Multiscale Waveform Inversion

Microseismic (MS) source location can help us obtain the fracture characteristics of a rock mass under a thermal-hydraulic-mechanical (THM) coupling environment. However, the commonly used ray-tracing-based location methods are easily affected by the large picking errors, multipath effects of travel time, and focusing and defocusing effects of rays in wavefield propagation, which are caused by the strong three-dimensional (3D) heterogeneity in mining areas. In this paper, we will introduce the rapidly developed waveform inversion-based location method into a mine MS field study. On this basis, the wavefields were modeled by utilizing a high-resolution 3D velocity model, a fractional-order Gaussian wavelet source-time function, and spectral element method (SEM) wavefield modeling. In order to reduce the computation cost of wavefield modeling, the 3D ray-shooting method based on a coarse grid was adopted to obtain an approximate MS event location. Based on this initial location, the multiscale waveform inversion strategy (from coarse to fine grids) and the L-BFGS iteration optimization algorithm were separately jointly selected to improve wavefield modeling speed efficiency and iterative convergence rate. Then, the IMS MS monitoring system set in the Yongshaba mine (China) and its tomographic 3D velocity model were used to conduct the synthetic test and application study. Results show that the source-time function based on the fractional-order Gaussian function wavelet can better fit complex recording waveforms compared with the conventional Ricker wavelet-based source-time function, and the waveform misfit during the L-BFGS iteration decreased rapidly. Furthermore, the multiscale waveform inversion method can obtain a similar location accuracy compared with the waveform inversion based on a single fine grid, and it can significantly decrease the iteration times and wavefield modeling computational cost. The average location error of the eight premeasured blasting events by the proposed approach is only 17.6 m, which can provide a good data research basis for analyzing MS event location and rock mass fracture characteristics in a mine.

Improving retrieval of crop biophysical properties in dryland areas using a multi-scale variational RTM inversion approach

Optical radiative transfer models (RTM) are used to study the relationship between vegetation biophysical properties and corresponding canopy reflectances. In this paper, a RTM is inverted with satellite based surface reflectance observations to estimate key vegetation biophysical properties such as leaf area index (LAI) and leaf chlorophyll content (Cab). The complexity of model inversion makes model optimization challenging, particularly in dryland areas where the vegetation signal may have become confounded by bright soil backgrounds. Add to this, general difficulties in separating vegetation properties contributing to the combined surface reflectance signal. In this study, using a Bayesian approach, the inversion approach is written as a cost function to minimize. The high non-linearity of the RTM makes the analytical resolution of the optimization unpractical. To overcome this problem, a new multi-scale variational inversion approach is proposed. It solves progressively the inversion problem by first simplifying it, then solving it, and then coming back progressively to the original inversion problem. The approach is tested over a dryland irrigated agricultural system composed of fields of alfalfa, Rhodes grass, carrots and maize. Validation is done comparing results to in-situ measurements and other commonly used retrieval methods. The retrieved properties are shown to be in good agreement with in-situ observations of Cab (RMSE = 0.2 μg cm−2 and R2 = 89%) and LAI (RMSE = 0.18 m2 m−2 and R2 = 92%), which is shown to be an improvement over other traditional variational techniques (Gradient, Newton, LUT and QNT).

Multi-centre, multi-vendor reproducibility of 7T QSM and R2* in the human brain: Results from the UK7T study

IntroductionWe present the reliability of ultra-high field T2* MRI at 7T, as part of the UK7T Network's “Travelling Heads” study. T2*-weighted MRI images can be processed to produce quantitative susceptibility maps (QSM) and R2* maps. These reflect iron and myelin concentrations, which are altered in many pathophysiological processes. The relaxation parameters of human brain tissue are such that R2* mapping and QSM show particularly strong gains in contrast-to-noise ratio at ultra-high field (7T) vs clinical field strengths (1.5–3T). We aimed to determine the inter-subject and inter-site reproducibility of QSM and R2* mapping at 7T, in readiness for future multi-site clinical studies. MethodsTen healthy volunteers were scanned with harmonised single- and multi-echo T2*-weighted gradient echo pulse sequences. Participants were scanned five times at each “home” site and once at each of four other sites. The five sites had 1× Philips, 2× Siemens Magnetom, and 2× Siemens Terra scanners. QSM and R2* maps were computed with the Multi-Scale Dipole Inversion (MSDI) algorithm (https://github.com/fil-physics/Publication-Code). Results were assessed in relevant subcortical and cortical regions of interest (ROIs) defined manually or by the MNI152 standard space. Results and DiscussionMean susceptibility (χ) and R2* values agreed broadly with literature values in all ROIs. The inter-site within-subject standard deviation was 0.001–0.005 ppm (χ) and 0.0005–0.001 ms−1 (R2*). For χ this is 2.1–4.8 fold better than 3T reports, and 1.1–3.4 fold better for R2*. The median ICC from within- and cross-site R2* data was 0.98 and 0.91, respectively. Multi-echo QSM had greater variability vs single-echo QSM especially in areas with large B0 inhomogeneity such as the inferior frontal cortex. Across sites, R2* values were more consistent than QSM in subcortical structures due to differences in B0-shimming. On a between-subject level, our measured χ and R2* cross-site variance is comparable to within-site variance in the literature, suggesting that it is reasonable to pool data across sites using our harmonised protocol. ConclusionThe harmonized UK7T protocol and pipeline delivers on average a 3-fold improvement in the coefficient of reproducibility for QSM and R2* at 7T compared to previous reports of multi-site reproducibility at 3T. These protocols are ready for use in multi-site clinical studies at 7T.