Nonlinear Tomography Research Articles

Invited commentary

Cryopreserved valve allografts offer superior hemodynamic performance in ventricular outflow reconstruction. Unfortunately, structural degeneration of the valve leaflets limits long-term durability. The performance and durability of any valve are dependent on the exquisitely complex tissue structure of the valve and annulus. Any disruption of the extracellular matrix structure will change the biomechanics of the tissue and may alter the function of any remaining viable cells. Schenke-Layland and colleagues [1Schenke-Layland K. Madershahian N. Riemann I. et al.Impact of cryopreservation on extracellular matrix structures of heart valve leaflets.Ann Thorac Surg. 2006; 81: 918-927Abstract Full Text Full Text PDF PubMed Scopus (84) Google Scholar] have made a step forward in our understanding of the structural deterioration of cryopreserved tissue. In their analysis of porcine pulmonary valves, standard biochemical assays suggested a preservation of the elastin and collagen content after cryopreservation. However, closer examination by multiphoton autofluorescence imaging demonstrates serious alteration in the structural arrangement of proteins. Interestingly, this disruption is most pronounced in the ventricularis layer in which both immunohistochemistry and nonlinear optical tomography demonstrated a loss of collagen, particularly type I. The cells in this layer were shown to be damaged (Fig 5) [1Schenke-Layland K. Madershahian N. Riemann I. et al.Impact of cryopreservation on extracellular matrix structures of heart valve leaflets.Ann Thorac Surg. 2006; 81: 918-927Abstract Full Text Full Text PDF PubMed Scopus (84) Google Scholar]. The mechanisms of this local valve structural alteration after cryopreservation need to be better understood, but is probably related to an activation of metalloproteinases (MMPs) upon thawing [2Kano M. Masuda Y. Tominaga T. et al.Collagen synthesis and collagenase activity of cryopreserved heart valves.J Thorac Cardiovasc Surg. 2001; 122: 706-711Abstract Full Text Full Text PDF PubMed Scopus (14) Google Scholar], and disruption of normal extracellular matrix metabolism by the valve interstitial cells [3Walker G.A. Masters K.S. Shah D.N. Anseth K.S. Leinwand L.A. Valvular myofibroblast activation by transforming growth factor-beta implications for pathological extracellular matrix remodeling in heart valve disease.Circ Res. 2004; 95: 253-260Crossref PubMed Scopus (312) Google Scholar], a function shown to be impaired in cryopreserved tissue [4Kneebone J.M. Lupinetti F.M. Procollagen synthesis by fresh and cryopreserved rat pulmonary valve grafts.J Thorac Cardiovasc Surg. 2000; 120: 596-603Abstract Full Text Full Text PDF PubMed Scopus (6) Google Scholar]. Side specific cell phenotypes and differences in extracellular matrix organization may account for the heterogeneity in extracellular matrix alteration [5Simmons C.A. Grant G.R. Manduchi E. Davies P.F. Spatial heterogeneity of endothelial phenotypes correlates with side-specific vulnerability to calcification in normal porcine aortic valves.Circ Res. 2005; 96: 792-799Crossref PubMed Scopus (209) Google Scholar, 6Scott M.J. Vesely I. Morphology of porcine aortic valve cusp elastin.J Heart Valve Dis. 1996; 5: 464-471PubMed Google Scholar]. In addition, the authors note a loss in collagen crimp, the tendency of unloaded collagen to have a rumpled configuration [7Parry D.A.D. The Molecular and fibrillar structure of collagen and its relationship to the mechanical-properties of connective-tissue.Biophysical Chemistry. 1988; 29: 195-209Crossref PubMed Scopus (203) Google Scholar]. Crimp is a major cause of the characteristic nonlinear mechanical response of soft tissue. Loss of this crimp may be due to a loss of the internal restoring force of the elastin as seen in Figure 5 [1Schenke-Layland K. Madershahian N. Riemann I. et al.Impact of cryopreservation on extracellular matrix structures of heart valve leaflets.Ann Thorac Surg. 2006; 81: 918-927Abstract Full Text Full Text PDF PubMed Scopus (84) Google Scholar]. The lack of crimp in the thawed cryopreserved valves suggests that the biomechanical properties of the ventricularis layer have been altered; however, no study to date has conducted the detailed biomechanical testing needed to verify this effect. The biological effects of the structural alteration caused by cryopreservation demonstrated in this article now have to be related to the performance and durability of allograft human valves. The consequences of these structural changes to the biomechanics and cell biology of the valve before implantation need to be investigated. Multiphoton tomography is a powerful new tool for determining molecular mechanisms and structural biology. Its applications to cardiovascular research will continue to increase as it can provide supporting evidence for structural deterioration in intact tissue, as shown in this article.

High-resolution teleseismic body wave tomography beneath SE-Romania - II. Imaging of a slab detachment scenario

Non-linear teleseismic bodywave tomography with data of the 1999 CALIXTO field experiment (Carpathian Arc Lithosphere X-Tomography) in Romania provides high-resolution imaging of the upper-mantle structure. In this paper, we present the relative P-wave velocity distribution of the lithosphere/asthenosphere system. Smearing from strong crustal velocity anomalies into the upper mantle is successfully suppressed by traveltime corrections with an a priori 3-D regional crustal velocity model (see Martin et al. 2005, herein referenced as paper 1). Our high-resolution image shows a high-velocity body beneath Vrancea and the Moesian platform with a NE-SW orientation between 70 and 200 km depth. Beneath 200 km a change in the orientation from NE-SW to N-S can be observed. The body reaches a maximum depth of about 350–370 km. The velocity perturbation is maximal between 110 and 150 km depth (5.2–5.8 per cent) and almost constant for depths beneath 200 km (3.2–3.8 per cent). As most authors of previous studies agree on Miocene subduction along the arc followed by soft continental collision we interpret the high-velocity body as the subducted, yet not fully detached slab. The NE-part of the slab appears to be mechanically coupled to the Moesian lithosphere and hosts the intermediate depth seismicity. In contrast the aseismic SW-part is interpreted as decoupled from the overlying lithosphere and torn off from the underlying lithospheric material beneath 200 km depth. Low velocity anomalies NW of the slab above 110 km depth are interpreted as a shallow asthenospheric upwelling. Further low-velocity anomalies are in agreement with a lithosphere-asthenosphere boundary at 110–150 km depth below the Moesian platform and deeper than 200 km under the East European platform (EEP). The tomographic images support models proposing slab rollback during subduction/collision, followed by slab steepening and lithospheric delamination. The different degrees of mechanical coupling of the slab to the overlying lithosphere allow to understand the loci of seismicity as volumes of stress concentration. Independent on the specifics of data interpretation our high-resolution image is a novel contribution to understand the process of ongoing lithospheric detachment associated with strong intermediate-depth seismicity in SE-Romania.

Linear and Nonlinear Microwave Tomography Approaches for Subsurface Prospecting: Validation on Real Data

In this letter, the capabilities of two tomographic approaches for subsurface prospecting have been tested against laboratory-controlled data. The first approach is a noniterative method based on the Born approximation, while the second one is a nonlinear iterative approach. Despite some simplifications adopted in modeling the scenario, both approaches have provided satisfying results.

Controlled source nonlinear tomography: A powerful tool to constrain tectonic models of the Southern Apennines orogenic wedge, Italy

The anatomy of the Southern Apennines is a matter of compelling debate. Both thick- and thin-skinned tectonic models are proposed due to paucity of deep seismic constraints. We present new and well-defined information on the velocity structure of the mountain range by using an innovative nonlinear tomographic technique applied to refraction– wide-angle reflection data. The velocity-interface model shows a high-velocity region, with values exceeding 7 km/s, at 8–9 km depth. Such large velocities cannot be related to sedimentary rocks, and imply the presence of shallow crystalline rocks, i.e., the basement involvement in the thrust belt. The integration of our results with other geophysical data (local earthquake tomography, Bouguer and magnetic anomalies) confirms this interpretation, which strongly supports thick-skinned tectonics and has significant implications for the seismotectonics and hydrocarbon potential of the Southern Apennines. Our inversion approach can be effective in other orogenic wedges, when seismic reflection profiling fails to uniquely resolve deep complex structures.

Frechet Kernels for Imaging Regional Earth Structure Based on Three-Dimensional Reference Models

High-resolution images of three-dimensional (3D) seismicstructuresare not only of scientific interest, but also of practical importance in predicting strong ground motion after large earthquakes. Given the source and station distributions, resolutions in current regional seismic tomography studies have been limited by two types of simplifying practices: the adoption of high-frequency approximations such as the ray theory and the use of one-dimensional (1D) reference (starting) models. We have developed a new approach to compute accurate finite-frequency 3D Frechet (sensitivity) kernels of observed travel time and amplitude anomalies relative to 3D reference models. In our approach, we use a fourth-order staggered-grid finite- difference method to model the seismic-wave propagation in 3D media, and the reciprocity property of the Green's tensor to reduce the number of numerical simu- lations. This approach accounts for the perturbations in compressional- and shear- wave speeds in the same way, leading to a capability of inverting for the shear-wave speed directly from seismic data. The algorithm is readily parallelized to allow for realistic regional high-resolution 3D tomography inversions. We have implemented the algorithm for the Southern California Earthquake Center (SCEC) Community Velocity Model, SCEC CVM 3.0, a complex 3D model for Southern California in- cluding a number of sedimentary basins. By enabling the inversion of 3D structural perturbations to 3D reference models, our approach provides a practical means of iteratively solving the nonlinear regional tomography problems.

3-D Non-linear Travel-time Tomography: Imaging High Contrast Velocity Anomalies

In this paper we present an approach for 3-D travel-time tomography, which works well in reconstructing high contrast velocity anomalies in both location and strength. It uses a revised ‘irregular’ approach to the shortest-path method as the ray tracer and a damped minimum norm, and constrained least-squares CG approach as the inversion solver. In ray tracing, the advantages of the revised ‘irregular’ over the ‘regular’ approach are that the secondary nodes introduced on the cell surfaces significantly improve accuracy of computed travel times, without dramatically increasing the total number of cells and nodes; the tri-linear velocity function defined across the cell guarantees accurate ray tracing in a high velocity contrast medium; and the capacity to calculate a relatively large 3-D model, due to the fast run speed (at least one order of magnitude over the ‘regular’ approach) and less number of total nodes. The introduction of ‘soft’ and ‘hard’ bounds into the inversion process changes the conditioning and makes the solution meaningful in a physical sense. Thus the artifacts caused by noise and high velocity contrasts are substantially suppressed and the image quality is considerably improved, making the solution realistic with noisy or inconsistent travel-time data. Several numerical tests indicate that we can obtain good quality images even for high velocity contrast anomalies (say more than 20%) in the target region. This means the inversion algorithm is an efficient and effective procedure. Meanwhile, the inversion procedure is not very sensitive to the quality of the travel-time data, which is promising for practical usage.

Electromagnetic traveltime tomography: Application for reservoir characterization in the Lost Hills oil field, California

Electromagnetic (EM) traveltime tomography has been applied for reservoir characterization at the Lost Hills oil field, California. Four data sets at frequencies of 24, 90, 370, and 1000 Hz were obtained along a pair of monitoring boreholes located 80.5 m apart. Traveltime information was first extracted from these EM data sets using a wavefield transform with a ray series approximation. The conductivity contrast of each layer is no greater than two in the region of interest, so the first arrivals can be estimated within 5% error by the approximate scheme. A nonlinear traveltime tomography algorithm adopting a Fresnel zone concept was then applied to obtain the conductivity model between the boreholes. The resultant conductivity image represents the conductivity structure between the boreholes. This image is consistent with the results of both a finite-difference inversion and the induction log obtained prior to waterflooding. Comparing the two conductivity images with the induction logs, we observe major differences in the fracture-dominant resistive reservoir layer, which may have been caused by changes in reservoir condition before and after waterflooding.

Nonlinear modal method of crack localization

A simple scheme for crack localization is discussed that is relevant to nonlinear modal tomography based on the cross-modulation of two signals at different frequencies. The scheme is illustrated by a theoretical model, in which a thin plate or bar with a single crack is excited by a strong low-frequency wave and a high-frequency probing wave (ultrasound). The crack is assumed to be small relative to all wavelengths. Nonlinear scattering from the crack is studied using a general matrix approach as well as simplified models allowing one to find the nonlinear part of crack volume variations under the given stress and then the combinational wave components in the tested material. The nonlinear response strongly depends on the crack position with respect to the peaks or nodes of the corresponding interacting signals which can be used for determination of the crack position. Juxtaposing various resonant modes interacting at the crack it is possible to retrieve both crack location and orientation. Some aspects of inverse problem solutions are also discussed, and preliminary experimental results are presented.

High-resolution body wave tomography beneath the SVEKALAPKO array - II. Anomalous upper mantle structure beneath the central Baltic Shield

A number of different geodynamic models have been proposed to explain the early tectonic evolution of the Baltic Shield. To provide additional geophysical constraints on these models, we performed a teleseismic tomography traveltime inversion for the central part of the Baltic Shield. The SVEKALAPKO project is focused on the investigation of the lithosphere—asthenosphere structure down to 400 km depth under central Fennoscandia (Baltic Shield). A total of 143 stations were deployed including 15 permanent stations from the Finnish seismic network. The temporal network was composed of 40 broad-band and 88 short-period instruments distributed in a rectangular array of 1000 km by 900 km from 1998 August to 1999 May. The results are based on a non-linear teleseismic tomography algorithm. They reveal significant P-velocity variations (up to 4 per cent) throughout the SVEKALAPKO array. The most prominent feature is a positive anomaly that can be followed down to 250 km depth beneath the centre of the array. We interpret this anomaly as the signature of the tectosphere (Jordan 1978) beneath the Fennoscandian Shield. It correlates spatially with an anomalous high-velocity lower crust. Other shallow (crustal) anomalies can be correlated with magmatic events surrounding this nucleus of high velocity. Comparison of images before and after correction by crustal structure proves that this methodology yields solid and coherent tomographic results. Further observations of relative P traveltime residuals from six teleseismic events with different azimuths show delay variations of ±2.0 s between stations located in the North German basin and stations on the Svecofennian Shield.

Nonlinear modal methods for crack localization

A nonlinear method for locating defects in solid materials is discussed that is relevant to nonlinear modal tomography based on the signal cross-modulation. The scheme is illustrated by a theoretical model in which a thin plate or bar with a single crack is excited by a strong low-frequency wave and a high-frequency probing wave (ultrasound). A crack is considered as a small contact-type defect which does not perturb the modal structure of sound in linear approximation but creates combinational-frequency components whose amplitudes depend on their closeness to a resonance and crack position. Using different crack models, including the hysteretic ones, the nonlinear part of its volume variations under the given stress and then the combinational wave components in the bar can be determined. Evidently, their amplitude depends strongly on the crack position with respect to the peaks or nodes of the corresponding linear signals which can be used for localization of the crack position. Exciting the sample by sweeping ultrasound frequencies through several resonances (modes) reduces the ambiguity in the localization. Some aspects of inverse problem solution are also discussed, and preliminary experimental results are presented.

Neural network multi-criteria optimization image reconstruction technique (NN-MOIRT) for linear and non-linear process tomography

In this work, an analog neural network is utilized to develop a new image reconstruction technique for the linear as well as the non-linear process tomography. The ultrasonic computed tomography (CT) and the electrical capacitance tomography (ECT) are chosen to represent the linear and the non-linear tomography. The image reconstruction technique is based on a multi-criteria optimization, namely neural network multi-criteria optimization image reconstruction technique (NN-MOIRT). The optimization technique utilizes multi-objective functions: (a) the negative entropy function, (b) the function of the least weighted square error of projection (integral) values between the measured data and the estimated projection data from the reconstructed image, and (c) a smoothness function that gives a relatively small peakedness in the reconstructed image. The optimization image reconstruction problem is then solved using the Hopfield model with dynamic neural-network computing. The technique has been tested using simulated and measured data; this technique has shown significant improvement in accuracy and consistency compared with other available techniques for both linear and non-linear tomography.

Complex Morphology of Subducted Lithosphere in the Mantle below the Molucca Collision Zone from Non-linear Seismic Tomography

Results of seismic studies presented in previous publications depict two opposing subducted oceanic lithospheric slabs under the Molucca region. This unique structure is related to the arc-arc collision between the Halmahera and Sangihe arcs. Recently, we have revisited the complex subduction zone structure by employing a non-linear tomographic imaging technique in which 3-D ray tracing has been implemented. We have used P- as well as S-wave arrival times from carefully reprocessed global data set. The results provide some improvements in the positioning of wave-speed anomalies. Consistent with earlier results, the new P-wave model depicts the two opposing subducted slabs of the Molucca Sea plate. The intriguing new observation is that the westward dipping slab appears to penetrate into the lower mantle by taking the form of folded slab. We envisage that the folding behavior may have been caused by the shift of the whole subduction system in the Molucca region toward the Eurasian continent due to the westward thrust of the Pacific plate combined with the large left-lateral movement of the Sorong fault. The inversion of traveltime residuals of direct S phases strongly confirms the new observation.

Study on Method of Wavelet Multi‐Scale Crosshole Seismic Tomography in Complex Media

AbstractCrosshole seismic tomography in complex media is a very complex and nonlinear inverse problem. We generally cannot obtain a satisfactory clear image by using linearized tomographic method. This paper proposes a wavelet multiscale seismic tomography method. The forwarding traveltime is calculated by using the graph‐based ray tracing approach. The method effectively solves the difficulty of nonlinear tomography, overcomes the drawbacks of the linearized inverse methods and enhances the tomographic resolution. The results of physical modeling show that the method is suitable for complex media, has good practicability and effectiveness.

Resonant nonlinear magneto-optical effects in atoms

The authors review the history, current status, physical mechanisms, experimental methods, and applications of nonlinear magneto-optical effects in atomic vapors. They begin by describing the pioneering work of Macaluso and Corbino over a century ago on linear magneto-optical effects (in which the properties of the medium do not depend on the light power) in the vicinity of atomic resonances. These effects are then contrasted with various nonlinear magneto-optical phenomena that have been studied both theoretically and experimentally since the late 1960s. In recent years, the field of nonlinear magneto-optics has experienced a revival of interest that has led to a number of developments, including the observation of ultranarrow (1-Hz) magneto-optical resonances, applications in sensitive magnetometry, nonlinear magneto-optical tomography, and the possibility of a search for parity- and time-reversal-invariance violation in atoms.

Non-linear body wave teleseismic tomography along the TOR array

Summary The TOR project investigates the lithosphere–asthenosphere structure under the Tornquist Zone between Denmark and Sweden. Around 150 seismic stations (108 short-period, 28 broadband and 14 other permanent stations) were employed in a rectangular array along a 900 km long by 100 km wide strip across the Tornquist Zone from July 1996 to August 1997. The results obtained based on a non-linear teleseismic tomography algorithm reveal significant P-velocity variations (up to 5 per cent) along the TOR array from northern Germany to southern Sweden. Distinct lithospheric blocks are also recognized in the inversion results. Two inverse methods (singular value decomposition and a quadratic programming method) were implemented in order to investigate whether or not the lithospheric blocks and major boundaries in the inversion are required by the data or are artefacts of the inversion. According to the results, the lithosphere under northern Germany is thin but reaches to intermediate thicknesses of about 120 km in the Tornquist Zone area. Farther north in the Baltic Shield, more than 200 km of continental lithosphere is recognized in the model. Abrupt lateral P-velocity changes (maximum 5 per cent) are seen at both the southern and northern sides of the Tornquist Zone.

Comparison of algorithms for non-linear inverse 3D electrical tomography reconstruction

Non-linear electrical impedance tomography reconstruction algorithms usually employ the Newton–Raphson iteration scheme to image the conductivity distribution inside the body. For complex 3D problems, the application of this method is not feasible any more due to the large matrices involved and their high storage requirements. In this paper we demonstrate the suitability of an alternative conjugate gradient reconstruction algorithm for 3D tomographic imaging incorporating adaptive mesh refinement and requiring less storage space than the Newton–Raphson scheme. We compare the reconstruction efficiency of both algorithms for a simple 3D head model. The results show that an increase in speed of about 30% is achievable with the conjugate gradient-based method without loss of accuracy.

Optimal imaging with adaptive mesh refinement in electrical impedance tomography

In non-linear electrical impedance tomography the goodness of fit of the trial images is assessed by the well-established statistical χ2 criterion applied to the measured and predicted datasets. Further selection from the range of images that fit the data is effected by imposing an explicit constraint on the form of the image, such as the minimization of the image gradients. In particular, the logarithm of the image gradients is chosen so that conductive and resistive deviations are treated in the same way. In this paper we introduce the idea of adaptive mesh refinement to the 2D problem so that the local scale of the mesh is always matched to the scale of the image structures. This improves the reconstruction resolution so that the image constraint adopted dominates and is not perturbed by the mesh discretization. The avoidance of unnecessary mesh elements optimizes the speed of reconstruction without degrading the resulting images. Starting with a mesh scale length of the order of the electrode separation it is shown that, for data obtained at presently achievable signal-to-noise ratios of 60 to 80 dB, one or two refinement stages are sufficient to generate high quality images.

Electromagnetic traveltime tomography using an approximate wavefield transform

We present an imaging scheme for mapping cross‐hole electrical conductivity using nonlinear traveltime tomography. Data used are peak arrival time estimates based on an approximate wavefield transform of the synthetic frequency‐domain electromagnetic (EM) field. Direct transformation of frequency‐domain EM fields to wavefields is known to be an ill‐posed problem because the kernel of integral transform is highly damped. In this study, instead of solving such an unstable problem, we approximate the wavefield in the transformed domain via a ray series expansion. If reflected and refracted energy is weak compared to that of direct wave, picking of the peak arrival time may be reduced to estimating the coefficients of the leading term in the ray series expansion. This simplification is valid when the conductivity contrast between background medium and the target anomalous body is small. The first three terms in the expansion are identical to the closed‐form solution for the vertical magnetic field caused by a vertical magnetic dipole source in a homogeneous whole‐space. An adaptive simulated annealing scheme is used to estimate the coefficients of ray series. For a whole‐space, exact traveltime can be extracted using only four frequency samples in our approach, whereas the direct numerical wavefield transform needed at least ten frequencies to construct a reasonable waveform. Nonlinear traveltime tomography using thusly‐extracted peak arrivals from synthetic data shows a reasonable image of the conductivity structure between boreholes.

Seismic evidence for a mantle plume oceanwards of the Kamchatka-Aleutian trench junction

SUMMARY A non-linear iterative P-wave traveltime tomography has revealed a mantle plume originating at a depth of nearly 1000 km, rising across the 600 km discontinuity, and deflecting subhorizontally in the uppermost mantle presumably by shear flow due to the overlying moving plate. Data from the Geophysical Survey of Russia (1955–1997) were inverted jointly with the catalogues of International Seismological Centre and USGS National Earthquake Information Centre (1964– 1998). The result shows a 300–500 kmwide cylindrical low-velocity anomaly (yx2 per cent) that extends from a depth of greater than 900 km to shallower than 200 km. The anomaly is almost vertical at depths up to y400 km and rises obliquely to the north up to y200 km under the ocean floor near the northern end of Emperor seamounts. Above y300 km depth a subsidiary anomaly extends subhorizontally to the NW in fair agreement with the direction of movement of the Pacific Plate. The overlying seafloor is characterized by anomalously high heat flow, which may be attributed to the thermal effect of the mantle plume.

Three‐dimensional S wave velocity structure and Vp/Vs ratios in the New Madrid Seismic Zone

A three‐dimensional S wave velocity model for the New Madrid Seismic Zone (NMSZ) has been developed using nonlinear travel time tomography. The inversion utilized 5544 S wave arrival times from 720 earthquakes recorded by digital, three‐component stations deployed in the NMSZ over the time period 1989 through 1992. We imaged S wave velocity anomalies ranging from −5% to +8% relative to the starting one‐dimensional velocity model. Lowest S wave velocities are found south of Ridgley, Tennessee, in an area characterized by a high earthquake swarm rate and shallower than normal hypocenters. Two centers of higher than average S wave velocity are located west of the Mississippi river, north of Caruthersville, Missouri. The S wave model is similar to a P wave velocity model generated using the same earthquake data set. The similarity in ray coverage in both the P and S wave solutions allowed calculation of Vp/Vs ratios. Most of the seismicity in the NW trending central arm of the NMSZ is associated with normal Vp/Vs values that border regions with high Vp/Vs. North of Ridgely, high Vp/Vs values are associated with higher than average compressional and shear wave velocities and are interpreted to be due to mafic intrusions along the axis and edges of the Reelfoot rift. SE of Ridgley, the end of the central arm coincides with high Vp/Vs values that are due to a significant shear wave low‐velocity zone and are interpreted to be the result of highly fractured and fluid saturated crust.