Fresnel zone inversion for lateral heterogeneities in the earth

Yomogida, Kiyoshi

doi:10.1007/bf00876879

Cited by 71 publications

(51 citation statements)

References 12 publications

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“…The frequency-domain Frechet kernels or the partial derivatives of seismic signals in laterally heterogeneous earth models, as exemplified in (122) for the direct turning SH wave, have been proposed for use in the inversion of laterally heterogeneous structures using band-limited seismic data (Woodward 1992;Yomogida 1992). When the Frechet kernels within a sufficiently wide frequency band are combined, only the heterogeneous structure in the first Fresnel zone, a region around the geometrical ray path in which the phases of the scattered waves differ by less than n2/2 from that of the geometrical ray, contributes to the perturbation of the seismic signal.…”

Section: Discussionmentioning

confidence: 99%

Mode-sum to ray-sum transformation in a spherical and an aspherical earth

Zhao

Dahlen

1996

Geophysical Journal International

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S U M M A R YWe complete our series of studies on the duality between relatively high-frequency normal modes and seismic body waves by explicitly converting the normal-mode summation expressing the elastic response of a spherically symmetric earth model into a body-wave summation. The procedures in this conversion are discussed in detail for a crust-stripped version of model 1066A with a solid mantle, a fluid outer core and a solid inner core. The resulting body-wave responses, the Green tensors representing the various body waves, are in agreement with the well-documented results obtained using geometrical ray theory.The results derived for the spherically symmetric earth model are then used to obtain the first-order body-wave Green tensors in a laterally heterogeneous earth model based upon the Born approximation. The first-order effect of the coupling between normalmode multiplets is shown to be equivalent to the single scattering of seismic body waves by the lateral heterogeneity, as expected from numerous previous studies. We present compact expressions for the scattering matrix and the body-wave FrCchet kernels. A few numerical examples of the Frtchet kernels for monochromatic body waves are also provided.

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Section: Discussionmentioning

confidence: 99%

Mode-sum to ray-sum transformation in a spherical and an aspherical earth

Zhao

Dahlen

1996

Geophysical Journal International

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“…To go beyond the ray theory, it is necessary to take account of the finite-frequency effect when scale length has the same order of magnitude as the seismic wavelength. It is possible to use the scattering theory based on the Born or Rytov approximations (see, e.g., Woodhouse and Girnius (1982) for normal mode approach, Snieder (1988) for surfaces waves, and Dahlen et al (2000 andYomogida (1992) for body waves). Equation [13] shows that the sensitivity kernels are 1-D, meaning that only heterogeneities in the vertical plane containing the source and the receiver are taken into account, whereas, by using the scattering theory, it is possible to calculate 3-D kernels and consequently to take account of off-path heterogeneities.…”

Section: Finite-frequency Effectsmentioning

confidence: 99%

Deep Earth Structure - Upper Mantle Structure: Global Isotropic and Anisotropic Elastic Tomography

Montagner

2015

Treatise on Geophysics

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“…In a series of pioneering studies, Yomogida (1992), Dahlen et al (2000) and Dahlen & Baig (2002) used the ray approximation for the computation of body wave Fréchet kernels in laterally homogeneous media. In a series of pioneering studies, Yomogida (1992), Dahlen et al (2000) and Dahlen & Baig (2002) used the ray approximation for the computation of body wave Fréchet kernels in laterally homogeneous media.…”

Section: Body Wavesmentioning

confidence: 99%

Full Seismic Waveform Modelling and Inversion

Fichtner¹

2011

Advances in Geophysical and Environmental Mechanics and Mathematics

371

349

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The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: deblik, BerlinPrinted on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) To my family and Carolin ForewordOur planet is permanently vibrating, excited by oceans, atmosphere, earthquakes, or man-made sources. Luckily, Earth's physical properties are such that these vibrations -elastic waves to be more specific -often propagate to large distances carrying information on the medium they encounter along the way. The problem of making an educated guess at the subsurface structure from observations of ground motions is as old as instrumental seismology itself (so not that old, maybe a century or so). Let us call the problem seismic tomography akin to CT scanning in medicine, a field seismologists have always envied. Because of limitations in illuminating the Earth with sufficient coverage we have never obtained the sharp and detailed internal structures so familiar from medical imaging.Up to now we have mostly cut corners in the way we model and fit our seismic data. We typically reduce long, wiggly seismograms to a few bytes of information (e.g. travel times, phase velocities) and try to explain these data with approximate theories. This has been for a good reason. Our computers were simply not fast and big enough to allow the calculation of complete wave fields through 3D Earth structures. Frequently the data just do not warrant the use of sophisticated physics.The situation regarding computational power in connection with 3D wave propagation has dramatically changed in the past few years. Even on a global scale the calculation of wave fields across the complete observed frequency range is in sight. On smaller scales (continents, basins, volcanoes, reservoirs) we are already witnessing the emergence of 3D wave propagation as the tool for data modelling, inversion and parameter studies.This was Albert Tarantola's (and others) dream 25 years ago: just simulate the physics correctly and let the data (i.e. the misfit to a theoretical seismogram) decide whether the Earth model is good or not. In his world (the probabilistic approach) this should be done using a Monte Carlo-type approach: calculate zillions of models and use all the results to estimate parameters and uncertainties. Unfortunately, we are not there yet. We still need to resort to linearisations around (hopefully good) starting models and employ adjoint-type techniques to update our Earth models. Fortunately, in many situations, good starting models can be found, making iterative waveform inversion the preferred tool to improve our Earth models using most or all of the observed data. vii viii ForewordThe book in your hands is the first to provide a broad overview on how to solve the forward problem to calculate accurate seismograms in 3D Earth m...

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Fresnel zone inversion for lateral heterogeneities in the earth

Cited by 71 publications

References 12 publications

Mode-sum to ray-sum transformation in a spherical and an aspherical earth

Mode-sum to ray-sum transformation in a spherical and an aspherical earth

Deep Earth Structure - Upper Mantle Structure: Global Isotropic and Anisotropic Elastic Tomography

Full Seismic Waveform Modelling and Inversion

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