Towards Mapping the Three-Dimensional Distribution of Water in the Upper Mantle from Velocity and Attenuation Tomography
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This chapter contains sections titled: Introduction Conversion of Seismological Data to Geophysical Parameters Inversion Discussion Appendi X: Some Notes on Partial Derivatives AijKeywords:
Seismic Tomography
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Seismic Tomography
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SUMMARY 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 tomography models, 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 correlation with 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.
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This paper mainly reviews the methods of seismic waves used to acquire subsurface velocity structures. Despite appearance of new approaches, seismic tomography, especially multi-phases grid tomography has been widely used and has been regarded as one of the effective methods to understand the interior structure imaging of the earth. Future requirement for the seismic tomography is to improve the quality of primary observation data, i.e. to increase the seismic stations used to receive the seismic waves. Meanwhile, multiple geophysical approaches along with restriction from inversion can establish a much strict geophysical model, which can decrease the geophysical inversion and interpretation ambiguity. This is not only the general trend of geophysical exploration and research but the direction of seismic tomography imaging.
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Vertical seismic profile
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Earth structure
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Overview, Keiiti Aki mathematical introduction to seismic tomography, W.H.K. Lee and V. Pereyra waveform inversion of long-period seismic data for global structure, Xiang-Dong Li and Toshiro Tanimoto global inversions using normal modes and long-period surface waves, Roel Snieder surface wave tomography - velocity and Q, Ichiro Nakanishi teleseismic tomography - global modelling, Hiroshi Inoue teleseismic tomography - core-mantle boundary, Andrea Morelli iterative strategies for nonlinear travel-time tomography using global earthquake data, Wim Spakman solving large linearized tomographic problems, Guust Nolet imaging the upper mantle with partitioned nonlinear waveform inversion, Guust Nolet teleseismic imaging of the western United States upper mantle structure using simultaneous iterative reconstruction technique, Kenneth Dueker, et al seismic tomography of China, F. Liu and A. Jin teleseismic-wave tomography of Italy, Alessandro Amato, et all teleseismic tomography of continental rift zones, Paul M. Davis, et al teleseismic tomography - lithospheric structure of the San Andres fault system, Harley M. Benz and George Zandt imaging volcanoes using teleseismic tomography, H.M. Iyer and P.B. Dawson tomography using both local earthquakes and teleseisms - velocity and anisotropy - theory, K. Hirahara tomography of subduction zones using local and regional earthquakes and teleseisms, K. Hirahara and Akiko hasemi local earthquake tomography - velocities and Vp/Vs - theory, Clifford H. Thurber tomography in zones of collision - practical considerations and examples, Steven W. Roecker local earthquake tomography - earthquake source regions, Donna Eberhart-Phillips local tomography - volcanoes and accretionary plate boundary Iceland, Gillian R. Foulger and And Stuart Arnott local earthquake tomography - attenuation - some theory and results, C.O. Sanders active high resolution (NeHT) tomography - velocity and Q, J.R. Evans and J.J. Zucca refraction and wide-angle reflection tomography - theory and results, Robert L. Nowack and Lawrence W. Braile seismic tomography in marine refraction experiments, James s. MClain tomography using waveform fitting of body-waves, Albert Tarantola, et al controlled-source tomography for mining and engineering applications, N.R. Goulty.
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List of Contents.- 1 Seismic wave propagation and seismic tomography.- I: Basic Theory.- 2 The Radon transform and seismic tomography.- 3 Numerical solution of large, sparse linear algebraic systems arising from tomographic problems.- 4 On the validity of the ray approximation for interpreting delay times.- 5 Ray tracing algorithms in three-dimensional laterally varying layered structures.- II: Applications in Seismic Exploration.- 6 Inversion of travel times and seismic waveforms.- 7 Crosshole transmission tomography.- 8 Tomography from seismic profiles.- 9 Seismic rock properties for reservoir descriptions and monitoring.- III: Applications in Global Seismology.- 10 Seismic data collection platforms for satellite transmission.- 11 The harmonic expansion approach to the retrieval of deep Earth structure.- 12 Ray tracing for surface waves.- 13 Waveform tomography.- 14 Surface wave holography.- 15 Tomographic imaging of seismic sources.- References.
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Seismic refraction
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This paper describes the application of tomography to seismic travel-time inversion. There are various implementations of travel-time tomography. In reflection tomography, sources and receivers are on the surface of the Earth and the principal seismic events are reflections from subsurface velocity discontinuities. In transmission tomography, sources and/or receivers may be buried beneath the surface and the events correspond to direct, or unreflected, arrivals; this is the analogue of medical tomography. There are also cases in which both direct as well as reflected arrivals are important, such as in Vertical Seismic Profiling. The latter is a direct application of the first two, but is not discussed in any detail here. It is also shown how the iterative use of travel-time tomography and depth migration can produce much enhanced subsurface images. Examples of both transmission tomography and reflection tomography combined with depth migration illustrate the methods.
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Traveltime tomography is the main method by which the Earth's seismic velocity is determined on all scales, from the near-surface (<100 m) to the core. Usually traveltime tomography uses ray theory, an infinite-frequency approximation of wave propagation. A theory developed in global seismology to account for the finite-frequency nature of seismic data, known as finite-frequency traveltime tomography (FFTT), can theoretically provide a more accurate estimation of velocity. But the FFTT theory is generally not applicable to near-surface data because there is no reference velocity model known in advance that is capable of yielding synthetic waveforms that are close enough to the recorded seismograms to yield a reliable delay time. Also, there is usually no reference model for which the unknown velocity model represents a small (linear) perturbation from the reference model. This paper presents a frequency dependent form of non-linear traveltime tomography specifically designed for near-surface seismic data in which a starting model, iterative approach with recalculated travel paths at each iteration, and the calculation of a frequency-dependent total traveltime, as opposed to a delay time, are used. Frequency-dependent traveltime tomography (FDTT) involves two modifications to conventional traveltime tomography: (1) the calculation of frequency-dependent traveltimes using wavelength-dependent velocity smoothing (WDVS) and (2) the corresponding sensitivity kernels that arise from using WDVS. Results show that the former modification is essential to achieve significant benefits from FDTT, whereas the latter is optional in that similar results can be achieved using infinite-frequency kernels. The long seismic wavelengths relative to the total path lengths and the size of subsurface heterogeneities of typical near-surface data means the improvements over ray theory tomography are significant. The benefits of FDTT are demonstrated using conventional minimum-structure regularization techniques to address the issue of model non-uniqueness. For synthetic data, the estimated FDTT models are shown to be more accurate than the corresponding infinite-frequency-derived models. Both 2-D and 3-D applications of FDTT to real data from a near-surface study yield estimated models that contain more structure than the corresponding infinite-frequency-derived models. Applications of FDTT without regularization demonstrate the potential of the WDVS-derived sensitivity kernels to provide a natural smoothing of the velocity model and thereby allow the data alone to determine the final model structure.
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Smoothing
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