Generalized least-squares solutions to quasi-linear inverse problems with a priori information.

Matsu’ura, Mitsuhiro; Hirata, Naoshi

doi:10.4294/jpe1952.30.451

Cited by 60 publications

(39 citation statements)

References 17 publications

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“…(15) is the unique least-squares solution with minimum length of the solution vector for the underdetermined case (e.g. Matsu'ura and Hirata, 1982). Such a solution with minimum overall change in the system under investigation is often physically or chemically seen to be the most appropriate solution ("Occam's razor").…”

Section: The Svd Least-squares Solutionmentioning

confidence: 99%

Ocean carbon cycling during the past 130 000 years – a pilot study on inverse palaeoclimate record modelling

2016

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Abstract. What role did changes in marine carbon cycle processes and calcareous organisms play in glacial-interglacial variation in atmospheric pCO 2 ? In order to answer this question, we explore results from an ocean biogeochemical general circulation model. We attempt to systematically reconcile model results with time-dependent sediment core data from the observations. For this purpose, we fit simulated sensitivities of oceanic tracer concentrations to changes in governing carbon cycle parameters to measured sediment core data. We assume that the time variation in the governing carbon cycle parameters follows the general pattern of the glacial-interglacial deuterium anomaly. Our analysis provides an independent estimate of a maximum mean sea surface temperature drawdown of about 5 • C and a maximum outgassing of the land biosphere by about 430 Pg C at the Last Glacial Maximum as compared to pre-industrial times. The overall fit of modelled palaeoclimate tracers to observations, however, remains quite weak, indicating the potential of more detailed modelling studies to fully exploit the information stored in the palaeoclimatic archive. This study confirms the hypothesis that a decline in ocean temperature and a more efficient biological carbon pump in combination with changes in ocean circulation are the key factors for explaining the glacial CO 2 drawdown. The analysis suggests that potential changes in the export rain ratio POC : CaCO 3 may not have a substantial imprint on the palaeoclimatic archive. The use of the last glacial as an inverted analogue to potential ocean acidification impacts thus may be quite limited.A strong decrease in CaCO 3 export production could potentially contribute to the glacial CO 2 decline in the atmosphere, but this remains hypothetical.

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Section: The Svd Least-squares Solutionmentioning

confidence: 99%

Ocean carbon cycling during the past 130 000 years – a pilot study on inverse palaeoclimate record modelling

2016

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“…We used a singular value decomposition method to solve the inverse problem and followed Matsu'ura and Hirata (1982) to determine how many singu-8 lar values to keep in the reconstruction of the model. We inverted the following equations that relate phase velocity anisotropy to azimuthal anisotropy at depth:…”

Section: Forward and Inverse Problemmentioning

confidence: 99%

Seismic anisotropy changes across upper mantle phase transitions

Yuan¹,

Beghein²

2013

Earth and Planetary Science Letters

154

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The mantle transition zone is believed to play an important role in the thermochemical evolution of our planet and in its deep water cycle. Constraining mantle flow at these depths can help elucidate its nature and better understand mantle dynamics and the history of plate tectonics. Seismic anisotropy, i.e. the directional dependence of seismic wave velocity, provides us with the most direct constraints on mantle deformation. Its detection below ∼250 km depth is challenging, and it is often assumed that the deep upper mantle is seismically isotropic due to a change in mantle deformation mechanism.Here, we present a global model of azimuthal anisotropy for the top 1000 km of the mantle. We used a dataset composed of fundamental and higher mode Rayleigh wave phase velocity maps, which provides resolution of azimuthal anisotropy to much greater depths than in previous studies. Our model unravels the presence of significant anisotropy in the transition zone, challenging common views of mantle deformation mechanisms, and reveals a striking correlation between changes in anisotropy amplitudes and in the fast * Corresponding author with the idea that the transition zone acts as a water filter.

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“…A small n s /n r ratio implies a slower convergence of the algorithm but helps perfom a sampling of the model space as thorough as possible to avoid getting trapped in a In this work, we first carried out regularized inversions of the surface wave data using eq. 15 and the singular value decomposition (SVD) method of Matsu'ura & Hirata (1982). This technique is described in details in .…”

Section: Modelingmentioning

confidence: 99%

A Bayesian approach to assess the importance of crustal corrections in global anisotropic surface wave tomography

Xing¹,

Beghein²

2015

Geophys. J. Int.

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SUMMARYSeveral recent studies have demonstrated the importance of crustal corrections when inverting surface wave data to model lateral variations in mantle radial anisotropy. It has also been shown that the choice of the prior crustal model to correct the data can strongly influence the anisotropy model and potentially lead to different geodynamic interpretations. In comparing tomographic models of radial anisotropy obtained from different crustal corrections, these studies did not, however, determine quantitative model uncertainties. Nevertheless, mantle models resulting from different prior crustal corrections are statistically different only if the posterior model errors stemming from the non-uniqueness of the inverse problem are smaller than the effect of the crustal correction itself.Here, we applied a model space search approach to global fundamental and higher mode Rayleigh and Love wave phase velocity maps to determine reliable, quantitative model uncertainties on seismic velocities and radial anisotropy. The technique employed enabled us to describe the model space with a posterior probability density function, and therefore to test whether models obtained from different crustal corrections are statistically different. We thus assessed the significance of the choice of the crustal model by comparing the posterior model errors to the differences in mantle structure resulting from different crustal corrections. We tested prior crustal models CRUST2.0, CRUST1.0, and 3SMAC.Our study shows that the use of prior crustal corrections from different crustal models yields significant discrepancies in mantle velocities around 50 km depth and in radial anisotropy down to 100 km. The impact of the crustal correction on radial anisotropy can extend down to 250 km in some locations. We found that choosing 3SMAC instead of the other crustal models has a stronger influence on the mantle model, but that CRUST1.0 and CRUST2.0 yield statistically identical anisotropy models at all depths, except at a few grid cells. Importantly, the effect of the crustal model is most significant in continental regionsand not so much beneath oceans, which has important consequences for determining the depth of continental roots. Our results therefore suggest that improving constraints on crustal structure in continents is essential for our understanding of continent formation.Our work also demonstrates that the prior crustal model does not significantly affect radial anisotropy and velocities at depths greater than 100 km. This implies that if geodynamic interpretations of radial anisotropy below 100 km depth were to account for tomographic model uncertainties, they would not depend on the choice of the prior crustal model. It is therefore important for geodynamicists and seismologists to work in concert and to put effort into determining quantitative tomographic model uncertainties before interpreting the results. Our results also caution against the use of 3SMAC to correct surface wave data for studies of the continental lithosphere, an...

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Generalized least-squares solutions to quasi-linear inverse problems with a priori information.

Cited by 60 publications

References 17 publications

Ocean carbon cycling during the past 130 000 years – a pilot study on inverse palaeoclimate record modelling

Ocean carbon cycling during the past 130 000 years – a pilot study on inverse palaeoclimate record modelling

Seismic anisotropy changes across upper mantle phase transitions

A Bayesian approach to assess the importance of crustal corrections in global anisotropic surface wave tomography

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Generalized least-squares solutions to quasi-linear inverse problems with a priori information.

Cited by 60 publications

References 17 publications

Ocean carbon cycling during the past 130 000 years – a pilot study on inverse palaeoclimate record modelling

Ocean carbon cycling during the past 130 000 years – a pilot study on inverse palaeoclimate record modelling

Seismic anisotropy changes across upper mantle phase transitions

A Bayesian approach to assess the importance of crustal corrections in global anisotropic surface wave tomography

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Product

Resources

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Ocean carbon cycling during the past 130 000 years – a pilot study on inverse palaeoclimate record modelling

Ocean carbon cycling during the past 130 000 years – a pilot study on inverse palaeoclimate record modelling