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Ping Tong - One of the best experts on this subject based on the ideXlab platform.
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frozen gaussian approximation for 3 d elastic wave equation and Seismic Tomography
Geophysical Journal International, 2019Co-Authors: James C Hateley, L Chai, Ping Tong, Xu YangAbstract:The purpose of this work is to generalize the frozen Gaussian approximation (FGA) theory to solve the 3-D elastic wave equation and use it as the forward modeling tool for Seismic Tomography with high-frequency data. FGA has been previously developed and verified as an efficient solver for high-frequency acoustic wave propagation (P-wave). The main contribution of this paper consists of three aspects: 1. We derive the FGA formulation for the 3-D elastic wave equation. Rather than standard ray-based methods (e.g. geometric optics and Gaussian beam method), the derivation requires to do asymptotic expansion in the week sense (integral form) so that one is able to perform integration by parts. Compared to the FGA theory for acoustic wave equation, the calculations in the derivation are much more technically involved due to the existence of both P- and S-waves, and the coupling of the polarized directions for SH- and SV-waves. In particular, we obtain the diabatic coupling terms for SH- and SV-waves, with the form closely connecting to the concept of Berry phase that is intensively studied in quantum mechanics and topology (Chern number). The accuracy and parallelizability of the FGA algorithm is illustrated by comparing to the spectral element method for 3-D elastic wave equation in homogeneous media; 2. We derive the interface conditions of FGA for 3-D elastic wave equation based on an Eulerian formulation and the Snell's law. We verify these conditions by simulating high-frequency elastic wave propagation in a 1-D layered Earth model. In this example, we also show that it is natural to apply the FGA algorithm to geometries with non-Cartesian coordinates; 3. We apply the developed FGA algorithm for 3-D Seismic { wave-equation-based traveltime Tomography and full waveform inversion, respectively
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time evolving Seismic Tomography the method and its application to the 1989 loma prieta and 2014 south napa earthquake area california
Geophysical Research Letters, 2017Co-Authors: Ping Tong, Dinghui Yang, Qinya LiuAbstract:We propose a time-evolving approach to conduct traveltime Seismic Tomography in the 1989 Mw 6.9 Loma Prieta earthquake and 2014 Mw 6.0 South Napa earthquake area, California. The recording period of the chosen Seismic data between January 1, 1967 and the day before the 2014 South Napa earthquake is divided into two time windows, separated by the 1989 Loma Prieta earthquake. In each time window the subsurface velocity structure is iteratively updated. Starting from the final model of the first time window, the velocity model has been successively improved throughout iterations in the second time window, indicating that the traveltime data of later time windows have provided extra information to refine the subsurface images. Strong heterogeneities are observed in the final P-wave velocity model. Both of the two large earthquakes occurred at transition zones in between high Vp and low Vp anomalies. In all, this study shows the effectiveness of the time-evolving Seismic Tomography method.
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3d nearly analytic central difference method for computation of sensitivity kernels of wave equation based Seismic Tomography
Bulletin of the Seismological Society of America, 2016Co-Authors: Xueyuan Huang, Ping Tong, Dinghui Yang, Yanjie ZhouAbstract:We propose a numerical method to perform forward‐modeling and sensitivity kernel computation in wave‐equation‐based Seismic Tomography. This method is an extension of the 2D nearly analytic central difference (NACD) method for solving the 3D acoustic wave equation. The 3D NACD method has fourth‐order accuracies both in time and space with only a three‐point stencil in each axis direction. Theoretical properties such as the stability criterion and the numerical dispersion relation were analyzed in detail. Relative to the fourth‐order Lax–Wendroff correction method and the fourth‐order staggered‐grid finite‐difference method, the 3D NACD method exhibits better performance in suppressing numerical dispersion. This was numerically confirmed by simulation of Seismic‐wave propagation in different models. Additionally, the 3D NACD method explicitly calculates the spatial gradients of the propagating wavefield, allowing a direct route to sensitivity kernel calculation. Using this method, waveform kernels and travel‐time kernels for direct arrival, single reflected phase, multiple reflected phase, and headwave are computed in a crust‐over‐mantle model. Numerical examples reveal that sensitivity kernel computation based on solving the full‐wave equation can accurately capture the interactions between wavefields and the Earth’s interior heterogeneous structures, and hence generate high‐accuracy sensitivity kernels for the subsequent tomographic inversion. Overall, the proposed method showed good performances for both forward‐modeling and sensitivity kernel calculation. This suggests that the 3D NACD method could serve as an efficient and accurate forwarding‐modeling tool for wave‐equation‐based Seismic Tomography.
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wave equation based travel time Seismic Tomography part 2 application to the 1992 landers earthquake m w 7 3 area
Solid Earth, 2014Co-Authors: Ping Tong, Dapeng Zhao, Xu Yang, Dinghui Yang, J Chen, Qiang LiuAbstract:Abstract. High-resolution 3-D P and S wave crustal velocity and Poisson's ratio models of the 1992 Landers earthquake (Mw 7.3) area are determined iteratively by a wave-equation-based travel-time Seismic Tomography (WETST) technique. The details of data selection, synthetic arrival-time determination, and trade-off analysis of damping and smoothing parameters are presented to show the performance of this new tomographic inversion method. A total of 78 523 P wave and 46 999 S wave high-quality arrival-time data from 2041 local earthquakes recorded by 275 stations during the period of 1992–2013 are used to obtain the final tomographic models, which cost around 10 000 CPU hours. Checkerboard resolution tests are conducted to verify the reliability of inversion results for the chosen Seismic data and the wave-equation-based travel-time Seismic Tomography method. Significant structural heterogeneities are revealed in the crust of the 1992 Landers earthquake area which may be closely related to the local Seismic activities. Strong variations of velocity and Poisson's ratio exist in the source regions of the Landers and three other nearby strong earthquakes. Most Seismicity occurs in areas with high-velocity and low Poisson's ratio, which may be associated with the seismogenic layer. Pronounced low-velocity anomalies revealed in the lower crust along the Elsinore, the San Jacinto, and the San Andreas faults may reflect the existence of fluids in the lower crust. The recovery of these strong heterogeneous structures is facilitated by the use of full wave equation solvers and WETST and verifies their ability in generating high-resolution tomographic models.
Qinya Liu - One of the best experts on this subject based on the ideXlab platform.
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time evolving Seismic Tomography the method and its application to the 1989 loma prieta and 2014 south napa earthquake area california
Geophysical Research Letters, 2017Co-Authors: Ping Tong, Dinghui Yang, Qinya LiuAbstract:We propose a time-evolving approach to conduct traveltime Seismic Tomography in the 1989 Mw 6.9 Loma Prieta earthquake and 2014 Mw 6.0 South Napa earthquake area, California. The recording period of the chosen Seismic data between January 1, 1967 and the day before the 2014 South Napa earthquake is divided into two time windows, separated by the 1989 Loma Prieta earthquake. In each time window the subsurface velocity structure is iteratively updated. Starting from the final model of the first time window, the velocity model has been successively improved throughout iterations in the second time window, indicating that the traveltime data of later time windows have provided extra information to refine the subsurface images. Strong heterogeneities are observed in the final P-wave velocity model. Both of the two large earthquakes occurred at transition zones in between high Vp and low Vp anomalies. In all, this study shows the effectiveness of the time-evolving Seismic Tomography method.
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Seismic Tomography adjoint methods time reversal and banana doughnut kernels
Geophysical Journal International, 2004Co-Authors: Jeroen Tromp, Carl Tape, Qinya LiuAbstract:SUMMARY We draw connections between Seismic Tomography, adjoint methods popular in climate and ocean dynamics, time-reversal imaging and finite-frequency ‘banana-doughnut’ kernels. We demonstrate that Frechet derivatives for tomographic and (finite) source inversions may be obtained based upon just two numerical simulations for each earthquake: one calculation for the current model and a second, ‘adjoint’, calculation that uses time-reversed signals at the receivers as simultaneous, fictitious sources. For a given model, m, we consider objective functions χ(m) that minimize differences between waveforms, traveltimes or amplitudes. For tomographic inversions we show that the Frechet derivatives of such objective functions may be written in the generic form , where δ ln m=δm/m denotes the relative model perturbation. The volumetric kernel Km is defined throughout the model volume V and is determined by time-integrated products between spatial and temporal derivatives of the regular displacement field s and the adjoint displacement field s†; the latter is obtained by using time-reversed signals at the receivers as simultaneous sources. In waveform Tomography the time-reversed signal consists of differences between the data and the synthetics, in traveltime Tomography it is determined by synthetic velocities, and in amplitude Tomography it is controlled by synthetic displacements. For each event, the construction of the kernel Km requires one forward calculation for the regular field s and one adjoint calculation involving the fields s and s†. In the case of traveltime Tomography, the kernels Km are weighted combinations of banana-doughnut kernels. For multiple events the kernels are simply summed. The final summed kernel is controlled by the distribution of events and stations. Frechet derivatives of the objective function with respect to topographic variations δh on internal discontinuities may be expressed in terms of 2-D kernels Kh and Kh in the form , where Σ denotes a solid-solid or fluid-solid boundary and ΣFS a fluid–solid boundary, and ∇Σ denotes the surface gradient. We illustrate how amplitude anomalies may be inverted for lateral variations in elastic and anelastic structure. In the context of a finite-source inversion, the model vector consists of the time-dependent elements of the moment-density tensor m(x, t). We demonstrate that the Frechet derivatives of the objective function χ may in this case be written in the form , where e† denotes the adjoint strain tensor on the finite-fault plane Σ. In the case of a point source this result reduces further to the calculation of the time-dependent adjoint strain tensor e† at the location of the point source, an approach reminiscent of an acoustic time-reversal mirror. The theory is illustrated for both tomographic and source inversions using a 2-D spectral-element method.
Dinghui Yang - One of the best experts on this subject based on the ideXlab platform.
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time evolving Seismic Tomography the method and its application to the 1989 loma prieta and 2014 south napa earthquake area california
Geophysical Research Letters, 2017Co-Authors: Ping Tong, Dinghui Yang, Qinya LiuAbstract:We propose a time-evolving approach to conduct traveltime Seismic Tomography in the 1989 Mw 6.9 Loma Prieta earthquake and 2014 Mw 6.0 South Napa earthquake area, California. The recording period of the chosen Seismic data between January 1, 1967 and the day before the 2014 South Napa earthquake is divided into two time windows, separated by the 1989 Loma Prieta earthquake. In each time window the subsurface velocity structure is iteratively updated. Starting from the final model of the first time window, the velocity model has been successively improved throughout iterations in the second time window, indicating that the traveltime data of later time windows have provided extra information to refine the subsurface images. Strong heterogeneities are observed in the final P-wave velocity model. Both of the two large earthquakes occurred at transition zones in between high Vp and low Vp anomalies. In all, this study shows the effectiveness of the time-evolving Seismic Tomography method.
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3d nearly analytic central difference method for computation of sensitivity kernels of wave equation based Seismic Tomography
Bulletin of the Seismological Society of America, 2016Co-Authors: Xueyuan Huang, Ping Tong, Dinghui Yang, Yanjie ZhouAbstract:We propose a numerical method to perform forward‐modeling and sensitivity kernel computation in wave‐equation‐based Seismic Tomography. This method is an extension of the 2D nearly analytic central difference (NACD) method for solving the 3D acoustic wave equation. The 3D NACD method has fourth‐order accuracies both in time and space with only a three‐point stencil in each axis direction. Theoretical properties such as the stability criterion and the numerical dispersion relation were analyzed in detail. Relative to the fourth‐order Lax–Wendroff correction method and the fourth‐order staggered‐grid finite‐difference method, the 3D NACD method exhibits better performance in suppressing numerical dispersion. This was numerically confirmed by simulation of Seismic‐wave propagation in different models. Additionally, the 3D NACD method explicitly calculates the spatial gradients of the propagating wavefield, allowing a direct route to sensitivity kernel calculation. Using this method, waveform kernels and travel‐time kernels for direct arrival, single reflected phase, multiple reflected phase, and headwave are computed in a crust‐over‐mantle model. Numerical examples reveal that sensitivity kernel computation based on solving the full‐wave equation can accurately capture the interactions between wavefields and the Earth’s interior heterogeneous structures, and hence generate high‐accuracy sensitivity kernels for the subsequent tomographic inversion. Overall, the proposed method showed good performances for both forward‐modeling and sensitivity kernel calculation. This suggests that the 3D NACD method could serve as an efficient and accurate forwarding‐modeling tool for wave‐equation‐based Seismic Tomography.
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wave equation based travel time Seismic Tomography part 2 application to the 1992 landers earthquake m w 7 3 area
Solid Earth, 2014Co-Authors: Ping Tong, Dapeng Zhao, Xu Yang, Dinghui Yang, J Chen, Qiang LiuAbstract:Abstract. High-resolution 3-D P and S wave crustal velocity and Poisson's ratio models of the 1992 Landers earthquake (Mw 7.3) area are determined iteratively by a wave-equation-based travel-time Seismic Tomography (WETST) technique. The details of data selection, synthetic arrival-time determination, and trade-off analysis of damping and smoothing parameters are presented to show the performance of this new tomographic inversion method. A total of 78 523 P wave and 46 999 S wave high-quality arrival-time data from 2041 local earthquakes recorded by 275 stations during the period of 1992–2013 are used to obtain the final tomographic models, which cost around 10 000 CPU hours. Checkerboard resolution tests are conducted to verify the reliability of inversion results for the chosen Seismic data and the wave-equation-based travel-time Seismic Tomography method. Significant structural heterogeneities are revealed in the crust of the 1992 Landers earthquake area which may be closely related to the local Seismic activities. Strong variations of velocity and Poisson's ratio exist in the source regions of the Landers and three other nearby strong earthquakes. Most Seismicity occurs in areas with high-velocity and low Poisson's ratio, which may be associated with the seismogenic layer. Pronounced low-velocity anomalies revealed in the lower crust along the Elsinore, the San Jacinto, and the San Andreas faults may reflect the existence of fluids in the lower crust. The recovery of these strong heterogeneous structures is facilitated by the use of full wave equation solvers and WETST and verifies their ability in generating high-resolution tomographic models.
Dapeng Zhao - One of the best experts on this subject based on the ideXlab platform.
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wave equation based travel time Seismic Tomography part 2 application to the 1992 landers earthquake m w 7 3 area
Solid Earth, 2014Co-Authors: Ping Tong, Dapeng Zhao, Xu Yang, Dinghui Yang, J Chen, Qiang LiuAbstract:Abstract. High-resolution 3-D P and S wave crustal velocity and Poisson's ratio models of the 1992 Landers earthquake (Mw 7.3) area are determined iteratively by a wave-equation-based travel-time Seismic Tomography (WETST) technique. The details of data selection, synthetic arrival-time determination, and trade-off analysis of damping and smoothing parameters are presented to show the performance of this new tomographic inversion method. A total of 78 523 P wave and 46 999 S wave high-quality arrival-time data from 2041 local earthquakes recorded by 275 stations during the period of 1992–2013 are used to obtain the final tomographic models, which cost around 10 000 CPU hours. Checkerboard resolution tests are conducted to verify the reliability of inversion results for the chosen Seismic data and the wave-equation-based travel-time Seismic Tomography method. Significant structural heterogeneities are revealed in the crust of the 1992 Landers earthquake area which may be closely related to the local Seismic activities. Strong variations of velocity and Poisson's ratio exist in the source regions of the Landers and three other nearby strong earthquakes. Most Seismicity occurs in areas with high-velocity and low Poisson's ratio, which may be associated with the seismogenic layer. Pronounced low-velocity anomalies revealed in the lower crust along the Elsinore, the San Jacinto, and the San Andreas faults may reflect the existence of fluids in the lower crust. The recovery of these strong heterogeneous structures is facilitated by the use of full wave equation solvers and WETST and verifies their ability in generating high-resolution tomographic models.
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Seismic Tomography and geochemical evidence for lunar mantle heterogeneity: Comparing with Earth
Global and Planetary Change, 2012Co-Authors: Dapeng Zhao, Tomoko Arai, Lucy Liu, Eiji OhtaniAbstract:Abstract We present Seismic Tomography and geochemical evidence for the existence of significant lateral heterogeneities in the lunar mantle and make a comparison with the Earth's heterogeneity and Seismicity. The Procellarum KREEP Terrane (PKT) is a unique province on the nearside of the Moon. It constitutes only about 15% or less of the lunar surface, but appears to owe a large portion of the Moon's radioactive heat-producing elements. We found a correlation between the Thorium (Th) abundance distribution and Seismic Tomography of the lunar nearside. The area with high Th abundance exhibits a distinct low shear-wave velocity, and the low-velocity anomaly extends down to 300–400 km depth below the PKT, suggesting that the thermal and compositional anomaly has a depth extent of 300–400 km in the lunar mantle. The distribution of deep moonquakes shows a correlation with the Seismic-velocity variations in the deep lunar mantle, similar to the earthquakes which are affected or controlled by structural heterogeneities in the terrestrial crust and upper mantle. The presence of deep moonquakes and Seismic-velocity heterogeneities in the mantle implies that the interior of the present Moon may be still thermally active.
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Multiscale Seismic Tomography and mantle dynamics
Gondwana Research, 2008Co-Authors: Dapeng ZhaoAbstract:Abstract In this article we first introduce the methodology of multiscale Seismic Tomography and the way to interpret the obtained tomographic images, and then review the significant recent results of multiscale Seismic Tomography with emphasis on mantle plumes and subducting slabs. Global and regional Tomography shows that most of the slab materials under Western Pacific and East Asia are stagnant in the mantle transition zone before finally collapsing down to the core–mantle boundary as a result of large gravitational instability from phase transitions. Local and teleSeismic Tomography studies have imaged clearly the subducting slabs and arc magma chambers in the upper-mantle wedge, indicating that geodynamic systems associated with arc magmatism and back-arc spreading are related to deep processes, such as convective circulation in the mantle wedge and dehydration reactions of the subducting slab. Because most hotspots are located in poorly instrumented continental and oceanic regions, 3-D crust and upper-mantle structure is determined for only a few hotspots such as Iceland, Yellowstone and Eifel which are covered by Seismic networks, and plume-like slow anomalies are revealed under those hotspots. Global Tomography has revealed deep mantle plumes under the major hotspots such as Hawaii, Iceland, Kerguelen, South Pacific and Africa. Strong lateral heterogeneities are revealed at the bottom of the mantle, which are associated with the deeply subducted slabs and the birth of mantle plumes. A thorough understanding of the deep Earth structure will only be achieved by a combination of more effective Seismic imaging techniques and dense coverage of global Seismic networks, particularly in the oceans.
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Mantle dynamics of Western Pacific and East Asia: Insight from Seismic Tomography and mineral physics
Gondwana Research, 2006Co-Authors: Dapeng Zhao, Shigenori Maruyama, Soichi OmoriAbstract:Abstract Recent results of high-resolution Seismic Tomography and mineral physics experiments are used to study mantle dynamics of Western Pacific and East Asia. The most important processes in subduction zones are the shallow and deep slab dehydration and the convective circulation (corner flow) processes in the mantle wedge. The combination of the two processes may have caused the back-arc spreading in the Lau basin, affected the morphology of the subducting Philippine Sea slab and its Seismicity under southwest Japan, and contributed to the formation of the continental rift system and intraplate volcanism in Northeast Asia, which are clearly visible in our tomographic images. Slow anomalies are also found in the mantle under the subducting Pacific slab, which may represent (a) small mantle plumes, (b) upwellings associated with the slab collapsing down to the lower mantle, or (c) sub-slab dehydration associated with deep earthquakes caused by the reactivation of large faults preserved in the slab. Combining tomographic images and earthquake hypocenters with phase diagrams in the systems of peridotite + water, we proposed a petrologic model for arc volcanism. Arc magmas are caused by the dehydration reactions of hydrated slab peridotite that supply water-rich fluids to the mantle wedge and cause partial melting of the convecting mantle wedge. A large amount of fluids can be released from hydrated MORB at depths shallower than 55 km, which move upwards to hydrate the wedge corner under the fore-arc, and never drag down to the deeper mantle along the slab surface. Slab dehydration reactions at 120 km depth are the antigorite-related 5 reactions which supply water-rich fluids for forming the volcanic front. Phase A and Mg-surssasite breakdown reactions at 200 and 300 km depths below 700 °C cause the second and third arcs, respectively. Moreover, the dehydration reactions of super-hydrous phase B, phases D and E at 500–660 km depths cause the fluid transportation to the mantle boundary layer (MBL) (410–660 km depth). The stagnant slabs extend from Japan to Beijing, China for over 1000 km long, indicating that the arc–trench system covers the entire region from the Japan trench to East Asia. We propose a big mantle wedge (BMW) model herein, where hydrous plumes originating from 410 km depth cause a series of intra-continental hot regions. Fluids derived from MBL accumulated by the double-sided subduction zones, rather than the India–Asia collision and the subsequent indentation into Asia, are the major cause for the active tectonics and mantle dynamics in this broad region.
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Tomography of the source area of the 1995 kobe earthquake evidence for fluids at the hypocenter
Science, 1996Co-Authors: Dapeng Zhao, Hiroo Kanamori, Hiroaki Negishi, Douglas A WiensAbstract:Seismic Tomography revealed a low Seismic velocity (-5%) and high Poisson's ratio (+6%) anomaly covering about 300 square kilometers at the hypocenter of the 17 January 1995, magnitude 7.2, Kobe earthquake in Japan. This anomaly may be due to an overpressurized, fluid-filled, fractured rock matrix that contributed to the initiation of the Kobe earthquake.
Bart Root - One of the best experts on this subject based on the ideXlab platform.
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Comparing global Tomography-derived and gravity-based upper mantle density models
Geophysical Journal International, 2020Co-Authors: Bart RootAbstract:Current Seismic Tomography models show a complex environment underneath the crust, corroborated by high-precision satellite gravity observations. Both data sets are used to independently explore the density structure of the upper mantle. However, combining these two data sets proves to be challenging. The gravity-data has an inherent insensitivity in the radial direction and Seismic Tomography has a heterogeneous data acquisition, resulting in smoothed Tomography models with de-correlation between different models for the mid-to-small wavelength features. Therefore, this study aims to assess and quantify the effect of regularization on a Seismic Tomography model by exploiting the high lateral sensitivity of gravity data. Seismic Tomography models, SL2013sv, SAVANI, SMEAN2 and S40RTS are compared to a gravity-based density model of the upper mantle. In order to obtain similar density solutions compared to the Seismic-derived models, the gravity-based model needs to be smoothed with a Gaussian filter. Different smoothening characteristics are observed for the variety of Seismic Tomography models, relating to the regularization approach in the inversions. Various S40RTS models with similar Seismic data but different regularization settings show that the smoothening effect is stronger with increasing regularization. The type of regularization has a dominant effect on the final Tomography solution. To reduce the effect of regularization on the Tomographymodels, an enhancement procedure is proposed. This enhancement should be performed within the spectral domain of the actual resolution of the Seismic Tomography model. The enhanced Seismic Tomography models show improved spatial correlationwith each other and with the gravity-based model. The variation of the density anomalies have similar peak-to-peak magnitudes and clear correlation to geological structures. The resolvement of the spectral misalignment between tomographic models and gravity-based solutions is the first step in the improvement of multidata inversion studies of the upper mantle and benefit from the advantages in both data sets.