Tomographic Maps Research Articles

Adaptively parametrized surface wave tomography: methodology and a new model of the European upper mantle

SUMMARY In this study, we aim to close the gap between regional and global traveltime tomography in the contextofsurfacewavetomographyoftheuppermantleimplementingtheprincipleofadaptive parametrization. Observations of seismic surface waves are a very powerful tool to constrain the3-DstructureoftheEarth’suppermantle,includingitsanisotropy,becausetheysamplethis volumeefficientlyduetotheirsensitivityoverawidedepthrangealongtheraypath.Onaglobal scale, surface wave tomography models are often parametrized uniformly, without accounting for inhomogeneities in data coverage and, as a result, in resolution, that are caused by effective under- or overparametrization in many areas. If the local resolving power of seismic data is not taken into account when parametrizing the model, features will be smeared and distorted in tomographic maps, with subsequent misinterpretation. Parametrization density has to change locally,formodelstoberobustlyconstrainedwithoutlosinganyaccurateinformationavailable in the best sampled regions. We have implemented a new algorithm for upper mantle surface wave tomography, based on adaptive-voxel parametrization, with voxel size defined by both the ‘hit count’ (number of observations sampling the voxel) and ‘azimuthal coverage’ (how welldifferentazimuthswithrespecttothevoxelarecoveredbythesource-stationdistribution). High image resolution is achieved in regions with dense data coverage, while lower image resolution is kept in regions where data coverage is poorer. This way, parametrization is everywhere tuned to optimal resolution, minimizing both the computational costs, and the non-uniqueness of the solution. The spacing of our global grid is locally as small as ∼50 km. We apply our method to identify a new global model of vertically and horizontally polarized shear velocity, with resolution particularly enhanced in the European lithosphere and upper mantle. We find our new model to resolve lithospheric thickness and radial anisotropy better than earlier results based on the same data. Robust features of our model include, for example, the Trans-European Suture Zone, the Panonnian Basin, thinned lithosphere in the Aegean and Western Mediterranean, possible small-scale mantle upwellings under Iberia and Massif Central, subduction under the Aegean arc and a very deep cratonic root underneath southern Finland.

A wireless impedance analyzer for automated tomographic mapping of a nanoengineered sensing skin

Polymeric thin-film assemblies whose bulk electrical conductivity and mechanical performance have been enhanced by single-walled carbon nanotubes are proposed for measuring strain and corrosion activity in metallic structural systems. Similar to the dermatological system found in animals, the proposed self-sensing thin-film assembly supports spatial strain and pH sensing via localized changes in electrical conductivity. Specifically, electrical impedance tomography (EIT) is used to create detailed mappings of film conductivity over its complete surface area using electrical measurements taken at the film boundary. While EIT is a powerful means of mapping the sensing skin`s spatial response, it requires a data acquisition system capable of taking electrical impedance measurements on a large number of electrodes. A low-cost wireless impedance analyzer is proposed to fully automate EIT data acquisition. The key attribute of the device is a flexible sinusoidal waveform generator capable of generating regulated current signals with frequencies from near-DC to 20 MHz. Furthermore, a multiplexed sensing interface offers 32 addressable channels from which voltage measurements can be made. A wireless interface is included to eliminate the cumbersome wiring often required for data acquisition in a structure. The functionality of the wireless impedance analyzer is illustrated on an experimental setup with the system used for automated acquisition of electrical impedance measurements taken on the boundary of a bio-inspired sensing skin recently proposed for structural health monitoring.

Analysis and 3D visualization of Mediterranean subsurface karst features based on tomographic mapping (Zominthos, Central Crete)

Analysis and 3D visualization of Mediterranean subsurface karst features based on tomographic mapping (Zominthos, Central Crete)

S-Wave Velocities of the Lithosphere–Asthenosphere System in the Caribbean Region

An overview of the S-wave velocity (V s) structural model of the Caribbean with a resolution of 2° × 2° is presented. New tomographic maps of Rayleigh wave group velocity dispersion at periods ranging from 10 to 40 s were obtained as a result of the frequency time analysis of seismic signals of more than 400 ray-paths in the region. For each cell of 2° × 2°, group velocity dispersion curves were determined and extended to 150 s by adding data from a larger scale tomographic study (Vdovin et al., Geophys. J. Int 136:324–340, 1999). Using, as independent a priori information, the available geological and geophysical data of the region, each dispersion curve has been inverted by the “hedgehog” non-linear procedure (Valyus, Determining seismic profiles from a set of observations (in Russian), Vychislitielnaya Seismologiya 4, 3–14. English translation: Computational Seismology (V.I. Keylis-Borok, ed.) 4:114–118, 1968), in order to compute a set of V s versus depth models up to 300 km of depth. Because of the non-uniqueness of the solutions for each cell, a local smoothness optimization has been applied to the whole region in order to choose a three-dimensional model of V s, satisfying this way the Occam's razor concept. Several known and some new main features of the Caribbean lithosphere and asthenosphere are shown on these models such as: the west directed subduction zone of the eastern Caribbean region with a clear mantle wedge between the Caribbean lithosphere and the subducted slab; the complex and asymmetric behavior of the crustal and lithospheric thickness in the Cayman ridge; the predominant oceanic crust in the region; the presence of continental type crust in Central America, and the South and North America plates; as well as the fact that the bottom of the upper asthenosphere gets shallower going from west to east.

Three‐dimensional tomographic mapping related to primary stability and structural miniscrew characteristics

To evaluate the maxilla, mandible, and cortical plates on computerized tomographic (CT) scans to achieve accurate three-dimensional bone thickness measurements. We selected the CT scans of 25 subjects (among 102), aged 18-58 years (10 men, 15 women), with nearly complete dentition. We performed interradicular and bucco-lingual (including cortical plate thickness) measurements in dental areas distal to the canines in both alveolar arches, at three levels (5, 8, and 11 mm) from the alveolar ridge. The mean thicknesses of the cortical plates in the maxilla were 1.10 mm buccally and 1.27 mm on the palatal side (p < 0.05). In the mandible, cortical plates were 2.23 mm buccally and 2.02 mm lingually. Mandibular buccal and lingual cortical plates became thicker distally in the second and third molar areas. There was considerable variation in cortical thickness (from 0.25 to 5.50 mm). Based on interradicular distances, only 13% of measured sites in the maxilla were suitable for miniscrew insertion (≥3.3 mm), but 63% of sites were suitable in the mandible. This study showed considerable individual variation in bone thickness. Our data suggested that the palatal/lingual side may provide greater primary stability for miniscrews. The palatal area, between the second upper bicuspid and the first molar, appeared to be the most suitable area for tapered 7- to 9-mm miniscrews, starting at 1.5-2 mm from the alveolar crest.

Surface Wave Path Corrections and Source Inversions in Southern California

The cut-and-paste (CAP) method for retrieving earthquake source parameters has proven useful in many regions. Since CAP breaks three-component data into Pnl and surface wave segments and models them separately, imperfect 1D Green’s functions can be effectively used to model the records and determine source parameters. The resultant time shifts for different segments, for example, Pnl or surface waves, can provide valuable data for improving the velocity model or Green’s functions. Moreover, if these shifts can be known from empirical path calibrations or estimated from a tomographic map, we can recover both source mechanism and location with an extended procedure CAPloc (Tan et al., 2006). Here we present a complete workflow from path calibration to source inversion in southern California. In particular, we use the CAP results from about 160 events with known locations to derive the Rayleigh and Love wave group velocity maps. We take a tomographic approach to solve for lateral velocity variations in 10 km size cells in a uniformly 12 km thick seismogenic layer. Velocity variations of up to 15% are observed and the patterns correlate well with some geological features. Synthetic surface waves for 2D cuts throughout the model with a finite difference approach show significant improvement over 1D synthetics in fitting surface wave travel times, but little difference in waveforms, which suggests 1D synthetics are sufficient in modeling with simple time shifts. This simplification allows source inversion for both mechanism and location to be easily obtained with CAPloc. Finally, we test the effectiveness of CAPloc in determining source parameters, including both mechanisms and locations with such calibration maps in poorly monitored situations. In particular, we focus on two station inversions with two pioneer stations PAS and GSC, which have appropriate recordings since 1960. Considerable success is achieved when the events are bracketed.

Crustal structure beneath Hudson Bay from ambient-noise tomography: implications for basin formation

SUMMARY The Hudson Bay basin is the least studied of four major Phanerozoic intracratonic basins in North America and the mechanism by which it formed remains ambiguous. We investigate the crustal structure of Hudson Bay based on ambient-noise tomography, using 21 months of continuous recordings from 37 broad-band seismograph stations that encircle the Bay. Green's functions that emerge from the cross correlation of these ambient noise recordings are dominated by fundamental-mode Rayleigh waves. In the microseismic period band (5–20 s), these signals are most prominently expressed in certain preferred azimuths indicative of stationary coastal source regions in southern Alaska and Labrador. Seasonal variations are subtle but consistent with more energetic noise sources during winter months, when wave heights in the Pacific and north Atlantic are larger than in the summer. Noise emanating from Hudson Bay does not appear to contribute significantly to the cross correlograms. Group-velocity dispersion curves are obtained by time-frequency analysis of cross-correlation functions. We test and implement a signal-to-noise ratio (SNR) selection method for producing one-sided cross correlograms, which yields better-defined dispersion ridges than the standard two-sided averaging approach. Tomographic maps and cross sections obtained in the 5–40 s period range reveal significantly lower crustal velocities beneath Hudson Bay than in the bounding Archean Superior craton. The lowest mid-crustal velocities correspond to a previously determined region of maximum lithospheric stretching near the centre of the basin. Pseudosections extracted from the tomographic inversions along profiles across Hudson Bay provide the first compelling direct evidence for crustal thinning beneath the basin. Our results are consistent with a recent estimate of 3 km of crustal thinning, but not consistent with a proposed model for basin subsidence triggered by eclogitization of a remnant crustal root.

Moho map of South America from receiver functions and surface waves

We estimate crustal structure and thickness of South America north of roughly 40°S. To this end, we analyzed receiver functions from 20 relatively new temporary broadband seismic stations deployed across eastern Brazil. In the analysis we include teleseismic and some regional events, particularly for stations that recorded few suitable earthquakes. We first estimate crustal thickness and average Poisson's ratio using two different stacking methods. We then combine the new crustal constraints with results from previous receiver function studies. To interpolate the crustal thickness between the station locations, we jointly invert these Moho point constraints, Rayleigh wave group velocities, and regional S and Rayleigh waveforms for a continuous map of Moho depth. The new tomographic Moho map suggests that Moho depth and Moho relief vary slightly with age within the Precambrian crust. Whether or not a positive correlation between crustal thickness and geologic age is derived from the pre‐interpolation point constraints depends strongly on the selected subset of receiver functions. This implies that using only pre‐interpolation point constraints (receiver functions) inadequately samples the spatial variation in geologic age. The new Moho map also reveals an anomalously deep Moho beneath the oldest core of the Amazonian Craton.

Midperiod Rayleigh wave attenuation model for Asia

We present an attenuation model for midperiod Rayleigh waves in Central Asia and surrounding regions. This model is defined by maps of attenuation coefficient across the region of study in the period band 14–24 s. The model is constructed to characterize the regional variations in attenuation of seismic waves in the crust, which are related to the tectonic history of the studied territory, to calibrate the regional surface‐wave magnitude scale, and to extend the teleseismic 'surface‐wave magnitude – body wave magnitude' (Ms‐mb) discriminant to regional distances. The construction of the model proceeds in three stages. The first stage in model construction is the measurement of Rayleigh wave spectral amplitudes. We collected and processed waveform data for 200 earthquakes occurring from 2003 to 2006 inside and around Eurasia, and used records of about 135 broadband permanent and temporary stations. This data set provided a sufficient number of spectral amplitude measurements between 14 and 24 s periods for the construction of two–dimensional tomographic maps of attenuation coefficients. At the second stage of the work, the integral of attenuation coefficients along given paths is estimated using both inter‐station measurements and single‐station measurements corrected for source and receiver terms. The third stage includes the refining of source parameters, recalculation of attenuation coefficient integrals after this refinement, grooming of resulting coefficients, and multistage tomographic inversion of the data. Tomographic maps for the set of periods from 14 to 24 s, which exhibit clear correlation with geology and tectonics of the territory under study, were obtained. Validation of these maps using the inter‐station measurements confirms their accuracy in predicting the observations.

Experimental verification of tomographic phase-space imaging for beams with space-charge using a pinhole-scan

A model is described for tomographic phase-space mapping and emittance measurement in beams with space-charge. The tomographic results of an experiment with a 10 keV space-charge dominated electron beam are presented. The data are compared against a direct experimental sampling of the phase-space using a pinhole scan. It is found that the accuracy of the tomographic method is within 10% for beams with space-charge intensity less than 90%. With the aid of numerical simulation the observed similarities and differences between the tomography method and pinhole scan are discussed.

Sampling Bounds for 2-D Vector Field Tomography

The tomographic mapping of a 2-D vector field from line-integral data in the discrete domain requires the uniform sampling of the continuous Radon domain parameter space. In this paper we use sampling theory and derive limits for the sampling steps of the Radon parameters, so that no information is lost. It is shown that if Δx is the sampling interval of the reconstruction region and x max is the maximum value of domain parameter x, the steps one should use to sample Radon parameters ρ and θ should be: \(\Delta\rho\leq\Delta x/\sqrt{2}\) and \(\Delta\theta\leq\Delta x/((\sqrt{2}+2)|x_{\max}|)\). Experiments show that when the proposed sampling bounds are violated, the reconstruction accuracy of the vector field deteriorates. We further demonstrate that the employment of a scanning geometry that satisfies the proposed sampling requirements also increases the resilience to noise.

High resolution Rayleigh wave group velocity tomography in North China from ambient seismic noise

Abstract This study presents the results of the Rayleigh wave group velocity tomography in North-China performed using ambient seismic noise observed at 190 broadband and 10 very broadband stations of the North-China Seismic Array. All available vertical component time-series for the 14 months span between January, 2007 and February, 2008 are cross-correlated to obtain empirical Rayleigh wave Green functions that are subsequently processed, with the multiple filter method, to isolate the group velocity dispersion curves of the fundamental mode of Rayleigh wave. Tomographic maps, with a grid spacing of 0.25o×0.25o, are computed at the periods of 4.5s, 12s, 20s, 28s. The maps at short periods reveal an evident lateral heterogeneity in the curst of North-China, quite well in agreement with known geological and tectonic features. The North China Basin is imaged as a broad low velocity area, while the Taihangshan and Yanshan uplifts and Ordos block are imaged as high velocity zones, and the Quaternary intermountain basins show up as small low-velocity anomalies. The group velocity contours at 4.5s, 12s and 20s are consistent with the Bouguer gravity anomalies measured in the area of the Taihangshan fault, that cuts through the lower crust at least. Most of the historical strong earthquakes (M≥6.0) are located where the tomographic maps show zones with moderate velocity gradient.

Fresnel tomography and interferometric technique for characterizing Laguerre–Gaussian beams

The Fresnel tomograms of Laguerre–Gaussian beams are found and the relation of the two-point spatial correlation function with the tomographic map is discussed. The spatial distribution and signature of vorticity of Laguerre–Gaussian modes is analyzed by measuring the two-point spatial correlation function of the one-dimensional projection of the vortex field. An interferometric approach, based on a Fourier projection algorithm, for the experimental determination of the two-point correlation function of the full complex vortex field at the cross-section plane of the recorded interference pattern is also described; this approach allows one to characterize the vortex structure and spatial coherence along the direction of propagation.

Generalized phase-space tomography for intense beams

Tomographic phase-space mapping in an intense particle beam is reviewed. The diagnostic is extended to beams with space-charge by assuming linear forces and is implemented using either solenoidal or quadrupole focusing lattices. The technique is benchmarked against self-consistent simulation and against a direct experimental sampling of phase-space using a pinhole scan. It is demonstrated that tomography can work for time-resolved phase-space mapping and slice emittance measurement. The technique is applied to a series of proof-of-principle tests conducted at the University of Maryland.

Comparison of 4D tomographic mapping versus thin-shell approximation for ionospheric delay corrections for single-frequency GPS receivers over North America

The majority of navigation satellite receivers operate on a single frequency. They compensate for the ionospheric delay using either an ionospheric model which typically only corrects for 50% of the delay or a thin-shell map of the ionosphere. A 4D tomographic imaging technique is used to map the free electron density over the full-height of the ionosphere above North America during autumn 2003. The navigation solutions computed using correction based upon the thin-shell and the full-height maps are compared in this paper. The maps are used to calculate the excess propagation delay on the L1 frequency experienced by GPS receivers at selected locations across North America. The excess delay is applied to correct the single-frequency pseudorange observations at each location, and the improvements to the resulting positioning are calculated. It is shown that the thin-shell and full-height maps perform almost as well as a dual-frequency carrier-smoothed benchmark and for most receivers better than the unfiltered dual-frequency benchmark. The full-height corrections perform well and are considerably better than thin-shell corrections under extreme storm conditions.

Three-dimensional surface wave tomography for the upper crustal velocity structure of southern Korea using seismic noise correlations

The cross-correlation technique was applied to ambient seismic noises to investigate the upper crustal velocity structure of the southern Korean Peninsula based on surface wave group velocities. We used seismograms recorded continuously during August 2005 at 91 accelerograph stations in the southern Korean Peninsula. From the correlation results of 4095 data pairs, the arrival times of Green’s functions along paths between stations of pairs were measured in discrete bins of frequency bands with central frequencies of 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, and 0.45 Hz. The spatial distribution of arrival times for each frequency band bin was inverted to obtain a two-dimensional tomographic map of Rayleigh wave group velocity. For each tomographic cell of the maps, we derived dispersion curves by extracting group velocities at center frequencies of the 7 frequency band bins. Shear-wave velocity obtained by depth inversion of the dispersion curve at each cell produced a one-dimensional velocity profile at depths. After aligning the profiles corresponding to tomographic cells, we obtained a three-dimensional uppermost crustal velocity model at depths down to approximately 8 km in the southern Korean Peninsula. These results show low-velocity distributions in the Gyeongsang Basin, western Gyeonggi Massif, and the area of Jeju Island and its northeastern coast. The Okcheon Fold Belt and Yeongnam Massif have relatively high velocity distributions. The low-velocity distribution in the Gyeongsang Basin shrinks in northsouth direction at depths around 4 km and widens again with a tendency to migrate to the east as the depth is increased. However, the linear trend of low velocities in NNE-SSW direction at deeper depths (6.25–8.25 km) in the western area distinctively coincides with the western boundary of the Gyeongsang Basin. The background noise analysis in this study provided the constraining information for determination of depth variation in the shear-wave velocity distribution.

Radon transforms of the Wigner operator on hyperplanes

The generalization of tomographic maps to hyperplanes is considered. We find that the Radon transform of the Wigner operator in multi-dimensional phase space leads to a normally ordered operator in binomial distribution—a mixed-state density operator. Reconstruction of the Wigner operator is also feasible. The normally ordered form and the Weyl ordered form of the Wigner operator are used in our derivation. The operator quantum tomography theory is expressed in terms of some operator identities, with the merit of revealing the essence of the theory in a simple and concise way.

Experimental and numerical study of phase mixing of an intense beam

We study, experimentally and numerically, the relaxation of an initially nonuniform intense beam in an alternating-gradient transport line. A nonlinear distribution consisting of five interacting beamlets is created and tracked for longer than seven plasma periods with the help of tomographic phase-space mapping. Emittance growth is initially rapid, but slows down as the nonuniform distribution homogenizes in a few plasma periods. Both growth rates are found to depend on the beam current.

Correlation of nonisotropically distributed ballistic scalar diffuse waves in two dimensions.

Theorems indicating that a fully equipartitioned random wave field will have correlations equivalent to the Greens function that would be obtained in an active measurement are now legion. Studies with seismic waves, ocean acoustics, and laboratory ultrasound have confirmed this. So motivated, seismologists have evaluated apparent seismic travel times in correlations of ambient seismic noise and constructed impressive tomographic maps of seismic wave velocity, and even detected fractional secular changes in seismic wave speed at a level of 0.0001. Inasmuch as the random seismic waves used in these evaluations are usually not fully equipartitioned, it seems right to ask why it works so well, or even if the results are trustworthy. The usual wave field used in long-period seismology is due to distant ocean storms and is, even in the presence of scattering, not isotropic. Here an asymptotic evaluation of the effect, on apparent travel time in a correlation waveform, is made of nonisotropic distributions of ballistic specific intensity. It is shown that for station pairs separated by one or more wavelengths, that the effect is small. A formula is derived permitting estimations of error, and corrections to travel times. It is successfully compared to errors seen in synthetic waveforms.

Imaging sensor constellation for tomographic chemical cloud mapping

A sensor constellation capable of determining the location and detailed concentration distribution of chemical warfare agent simulant clouds has been developed and demonstrated on government test ranges. The constellation is based on the use of standoff passive multispectral infrared imaging sensors to make column density measurements through the chemical cloud from two or more locations around its periphery. A computed tomography inversion method is employed to produce a 3D concentration profile of the cloud from the 2D line density measurements. We discuss the theoretical basis of the approach and present results of recent field experiments where controlled releases of chemical warfare agent simulants were simultaneously viewed by three chemical imaging sensors. Systematic investigations of the algorithm using synthetic data indicate that for complex functions, 3D reconstruction errors are less than 20% even in the case of a limited three-sensor measurement network. Field data results demonstrate the capability of the constellation to determine 3D concentration profiles that account for ~?86%? of the total known mass of material released.