Generalized nonlinear inverse problems solved using the least squares criterion

Tarantola, Albert; Valette, Bernard

doi:10.1029/rg020i002p00219

Cited by 1,893 publications

(1,383 citation statements)

References 7 publications

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“…According to the non-linear least-squares inversion formula of Tarantola and Valette (1982), Roecker (1982), Roecker, et al (1987Roecker, et al ( , 1993 developed an inversion program, SPHYPIT90, which can be used for tomography with the travel time data of seismic phases. The relation between the seismic phases and the seismic wave velocity structure model can be written as…”

Section: Methods and Datamentioning

confidence: 99%

Earthquake relocation and 3-dimensional crustal structure of P-wave velocity in cen-tral-western China

Yang

Zheng

et al. 2004

Acta Seismologica Sinica

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A simultaneous inversion of earthquake relocation and three-dimensional crustal structure of P-wave velocity in central-western China (21°N~36°N, 98°E~112°E) were performed in this paper. The crustal P-wave velocity model and earthquake relocation for this region are obtained using P g and S g phase readings of 9 988 earthquakes from 1992 to 1999 recorded at 193 seismic stations within central-western China by SPHYPIT90 and SPHREL3D90 programs. A lateral inhomogeneous structure of P-wave velocity in this region was obtained. Obvious contrast of P-wave velocities was revealed on both sides of active fault zones. Relocated epicenters of 6 459 events show clear lineation along active faults, which indicated a close correlation between seismicity and the active faults in this region. Focal depths of 82% relocated events ranged from 0 to 20 km, which is in good agreement with that from double-difference earthquake location algorithm.

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Section: Methods and Datamentioning

confidence: 99%

Earthquake relocation and 3-dimensional crustal structure of P-wave velocity in cen-tral-western China

Yang

Zheng

et al. 2004

Acta Seismologica Sinica

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“…First, an iterative simulated downhill simplex annealing method [Press et al, 1992] is used to solve for the phase, amplitude, and propagation azimuth of the two waves, while velocity is constrained to a constant initial velocity model. A secondary linearized inversion [Tarantola and Valette, 1982] is then used to solve for corrections to the initial velocity model while simultaneously further refining wave parameters by minimizing misfit to observations in a least-squares sense.…”

Section: Phase Velocity Inversionmentioning

confidence: 99%

Lithospheric instability and the source of the Cameroon Volcanic Line: Evidence from Rayleigh wave phase velocity tomography

et al. 2015

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The Cameroon Volcanic Line (CVL) is a 1800 km long volcanic chain, extending SW-NE from the Gulf of Guinea into Central Africa, that lacks the typical age progression exhibited by hot spot-related volcanic tracks. This study investigates the upper mantle seismic structure beneath the CVL and surrounding regions to constrain the origin of volcanic lines that are poorly described by the classic plume model. Rayleigh wave phase velocities are measured at periods from 20 to 182 s following the two-plane wave methodology, using data from the Cameroon Seismic Experiment, which consists of 32 broadband stations deployed between 2005 and 2007. These phase velocities are then inverted to build a model of shear wave velocity structure in the upper mantle beneath the CVL. Results show that phase velocities beneath the CVL are reduced at all periods, with average velocities beneath the CVL deviating more than -2% from the regional average and +4% beneath the Congo Craton. This distinction is observed for all periods but is less pronounced for the longest periods measured. Inversion for shear wave velocity structure indicates a tabular low velocity anomaly directly beneath the CVL at depths of 50 to at least 200 km and a sharp vertical boundary with faster velocities beneath the Congo Craton. These observations demonstrate widespread infiltration or erosion of the continental lithosphere beneath the CVL, most likely caused by mantle upwelling associated with edge-flow convection driven by the Congo Craton or by lithospheric instabilities that develop due to the nearby edge of the African continent.

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“…The purpose is to find the most likely estimation to the true state (which is unknown) using the information provided by the chosen physical model and the available observational data considering both of their uncertainties and the limitations of both model and observations. Data-assimilation methods are based on, and can be derived from, Bayesian statistics, minimum variance, maximum likelihood, or least squares methods [Maybeck, 1979;Kalnay, 2003;Daley, 1991;Talagrand, 1997;Tarantola, 1987;Tarantola and Valette, 1982].…”

Section: Ensemble Kalman Filtermentioning

confidence: 99%

Identifying the radiation belt source region by data assimilation

et al. 2007

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[1] We describe how assimilation of radiation belt data with a simple radial diffusion code can be used to identify and adjust for unknown physics in the model. We study the dropout and the following enhancement of relativistic electrons during a moderate storm on 25 October 2002. We introduce a technique that uses an ensemble Kalman filter and the probability distribution of the forecast ensemble to identify if the model is drifting away from the observations and to find inconsistencies between model forecast and observations. We use the method to pinpoint the time periods and locations where most of the disagreement occurs and how much the Kalman filter has to adjust the model state to match the observations. Although the model does not contain explicit source or loss terms, the Kalman filter algorithm can implicitly add very localized sources or losses in order to reduce the discrepancy between model and observations. We use this technique with multisatellite observations to determine when simple radial diffusion is inconsistent with the observed phase space densities indicating where additional source (acceleration) or loss (precipitation) processes must be active. We find that the outer boundary estimated by the ensemble Kalman filter is consistent with negative phase space density gradients in the outer electron radiation belt. We also identify specific regions in the radiation belts (L* % 5-6 and to a minor extend also L* % 4) where simple radial diffusion fails to adequately capture the variability of the observations, suggesting local acceleration/loss mechanisms.

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Generalized nonlinear inverse problems solved using the least squares criterion

Cited by 1,893 publications

References 7 publications

Earthquake relocation and 3-dimensional crustal structure of P-wave velocity in cen-tral-western China

Earthquake relocation and 3-dimensional crustal structure of P-wave velocity in cen-tral-western China

Lithospheric instability and the source of the Cameroon Volcanic Line: Evidence from Rayleigh wave phase velocity tomography

Identifying the radiation belt source region by data assimilation

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