<i>P</i>wave amplitudes in a 3-D earth

Tibuleac, I. M.; Nolet, Guust; Caryl, Michaelson; Koulakov, I.

doi:10.1046/j.1365-246x.2003.01969.x

Cited by 24 publications

(16 citation statements)

References 18 publications

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“…Since variations in velocity and attenuation both affect wave amplitudes, a joint inversion for velocity and attenuation is called for. In addition, ray theory does not model the frequency dependence of the effects of focusing, which is observed in practice (Allen et al 1999;Tibuleac et al 2003;Sigloch & Nolet 2006). Attempts to eliminate the effects of focusing in surface waves were first made by Romanowicz (1990) and Durek et al (1993), and were recently followed by successful attempts to invert for velocity and attenuation jointly (Billien et al 2000;Dalton & Ekström 2006).…”

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confidence: 99%

Multiple-frequencySH-wave tomography of the western US upper mantle

Yu¹,

Sigloch²,

Nolet³

2009

Geophysical Journal International

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SUMMARY We estimate the SH‐wave velocity and attenuation structures of the western US upper mantle using the dense network of the USArray and new techniques: we observe a multiple‐frequency data set of both traveltime and amplitude anomalies, and interpret these with full 3‐D finite‐frequency sensitivity kernels. Amplitudes show stronger frequency dependence than traveltimes. We perform a joint inversion on the measured traveltime and amplitude anomalies, interpreting them in terms of velocity and attenuation heterogeneities. Aside from the expected clear division between the slow, tectonically active region in the west and the fast craton in the east, several interesting smaller velocity anomalies are observed. The subduction along the Cascades at 100–300 km depths shows lateral discontinuity, with a ‘slab hole’ (absence of fast anomalies) observed around 45°N. The delaminated Sierra Nevada Mountains root is observed to have sunk to 200 km depth. The Yellowstone plume seems to have an origin (weak slow velocity anomalies) near 1000 km depth, but the plume conduit seems to be interrupted by a fast anomaly, which is identified as a fragment of the Farallon slab. The S‐velocity model shows a trench‐perpendicular ‘slab gap’ (absence of fast anomalies) at almost the same location as in the P model recently published by Sigloch et al. (2008). The methodological improvements described in the first paragraph have several benefits. Amplitude data help to sharpen the edges of narrow velocity heterogeneities in the shallow upper mantle. The focusing effect from velocity heterogeneity dominates over that of attenuation and must be considered when interpreting amplitude anomalies. In general, velocity and attenuation heterogeneities correlate positively, suggesting that temperature plays a major role in forming the anomalies.

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confidence: 99%

Multiple-frequencySH-wave tomography of the western US upper mantle

Yu¹,

Sigloch²,

Nolet³

2009

Geophysical Journal International

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“…Tibuleac et al, 2003;Sigloch et al, 2006Sigloch et al, , 2008. Tibuleac et al, 2003;Sigloch et al, 2006Sigloch et al, , 2008.…”

Section: Amplitudesunclassified

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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“…The relative rms amplitude misfit between real and synthetic waveforms is defined through the equations where u i and u 0 i are assumed to be already windowed to a particular phase or a specific part of the seismogram. Tibuleac et al (2003) demonstrated that E rms for P waves contains information about the Earth's structure. The corresponding sensitivity kernels have been derived by Dahlen & Baig (2002).…”

Section: Interrelations Between Objective Functionals and Their Assmentioning

confidence: 99%

Theoretical background for continental- and global-scale full-waveform inversion in the time-frequency domain

Fichtner

Kennett

Igel

et al. 2008

Geophysical Journal International

249

179

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S U M M A R YWe propose a new approach to full seismic waveform inversion on continental and global scales. This is based on the time-frequency transform of both data and synthetic seismograms with the use of time-and frequency-dependent phase and envelope misfits. These misfits allow us to provide a complete quantification of the differences between data and synthetics while separating phase and amplitude information. The result is an efficient exploitation of waveform information that is robust and quasi-linearly related to Earth's structure. Thus, the phase and envelope misfits are usable for continental-and global-scale tomography, that is, in a scenario where the seismic wavefield is spatially undersampled and where a 3-D reference model is usually unavailable. Body waves, surface waves and interfering phases are naturally included in the analysis. We discuss and illustrate technical details of phase measurements such as the treatment of phase jumps and instability in the case of small amplitudes.The Fréchet kernels for phase and envelope misfits can be expressed in terms of their corresponding adjoint wavefields and the forward wavefield. The adjoint wavefields are uniquely determined by their respective adjoint-source time functions. We derive the adjoint-source time functions for phase and envelope misfits. The adjoint sources can be expressed as inverse time-frequency transforms of a weighted phase difference or a weighted envelope difference.In a comparative study, we establish connections between the phase and envelope misfits and the following widely used measures of seismic waveform differences: (1) cross-correlation time-shifts; (2) relative rms amplitude differences; (3) generalized seismological data functionals and (4) the L 2 distance between data and synthetics used in time-domain full-waveform inversion.We illustrate the computation of Fréchet kernels for phase and envelope misfits with data from an event in the West Irian region of Indonesia, recorded on the Australian continent. The synthetic seismograms are computed for a heterogeneous 3-D velocity model of the Australian upper mantle, with a spectral-element method. The examples include P body waves, Rayleigh waves and S waves, interfering with higher-mode surface waves. All the kernels differ from the more familar kernels for cross-correlation time-shifts or relative rms amplitude differences. The differences arise from interference effects, 3-D Earth's structure and waveform dissimilarities that are due to waveform dispersion in the heterogeneous Earth.

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Pwave amplitudes in a 3-D earth

Cited by 24 publications

References 18 publications

Multiple-frequencySH-wave tomography of the western US upper mantle

Multiple-frequencySH-wave tomography of the western US upper mantle

Full Seismic Waveform Modelling and Inversion

Theoretical background for continental- and global-scale full-waveform inversion in the time-frequency domain

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