Inverse Problem Theory and Methods for Model Parameter Estimation

Tarantola, Albert

doi:10.1137/1.9780898717921

Cited by 5,598 publications

(5,791 citation statements)

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“…It is obvious that we can retrieve the 3-D deformation and the volume changes included in X simultaneously by solving the Equation (5) with Least Square (LS) algorithm if M ≥ N. Although Equation (5) is over determined, it may be unstable because of ill-conditions [81,82]. To ensure the stability of LS inversion, a fit smoothness constraint should be involved in the model.…”

Section: -D Deformations and Volume Changes Inversionmentioning

confidence: 99%

Deriving 3-D Time-Series Ground Deformations Induced by Underground Fluid Flows with InSAR: Case Study of Sebei Gas Fields, China

Liu

Sun

et al. 2017

Remote Sensing

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Multi-temporal Interferometric Synthetic Aperture Radar (MT-InSAR) technique has proven to be a powerful tool for the monitoring of time-series ground deformations along the line-of-sight (LOS) direction. However, the one-dimensional (1-D) measurements cannot provide comprehensive information for interpreting the related geo-hazards. Recently, a novel method has been proposed to map the three-dimensional (3-D) deformation associated with underground fluid flows based on single-track InSAR LOS measurements and the deformation modeling associated with the Green's function. In this study, the method is extended in temporal domain by exploiting the MT-InSAR measurements, and applied for the first time to investigate the 3-D time series deformation over Sebei gas field in Qinghai, Northwest China with 37 Sentinel-1 images acquired during October 2014-July 2017. The estimated 3-D time series deformations provide a more complete view of ongoing deformation processes as compared to the 1-D time series deformations or the 3-D deformation velocities, which is of great importance for assessing the possible geohazards. In addition, the extended method allows for the retrieval of time series of fluid volume changes due to the gas extraction in the Sebei field, which agrees well with those from the PetroChina Qinghai Oilfield Company Yearbooks (PQOCYs). This provides a new way to study the variations of subsurface fluids at unprecedented resolution.

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Section: -D Deformations and Volume Changes Inversionmentioning

confidence: 99%

Deriving 3-D Time-Series Ground Deformations Induced by Underground Fluid Flows with InSAR: Case Study of Sebei Gas Fields, China

Liu

Sun

et al. 2017

Remote Sensing

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“…The velocity model which was used for this procedure was derived by 3D tomographic inversion performed by Martakis, (2003) in the study area. The earthquake location algorithm implemented in the program NLLoc follows the probabilistic formulation of inversion presented in Tarantola andValette, (1982) andTarantola, (1987), which produces comprehensive uncertainty and…”

Section: Location 3d (Nlloc)mentioning

confidence: 99%

Earthquake relocation for North-Western Greece using 3D crustal model; method comparison and seismotectonic interpretation.

et al. 2016

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A dense microseismic network was installed in Northwestern Greece for a period of eleven months. A total of 1368 events were recorded and located using a 1D model. These events were also used to derive a 3D velocity model for the area. This work presents results from further processing of the data using (a) simple location method of events in a 1D medium through Hypo71 standard procedure; (b) location via the probabilistic, non-linear earthquake location method in 3D medium; (c) relocation of the events using the Double - Difference method in 1D medium; and (d) the same relocation procedure invoking 3D medium. The application of different location methodologies results in slightly different locations, which are evaluated using as criterion the compactness of hypocenter distribution. The three point method was used in order to derive linear characteristics from the hypocenter distribution and the final results were compared against the focal mechanisms of the events as computed using the polarity method and the 3D velocity model. The combination of accurately computed hypocenters and focal mechanisms provides important information for the seismotectonics of Epirus

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“…Em, E b and E O are assumed to be Gaussian and then fully characterized by their covariance matrices Q, B and R [21]. Let Z denote a Gaussian stochastic vector depending on a space-time coordinate (x, t); Z = Z(x, t) and Z ′ = Z(x ′ , t ′ ) are random vectors on the two given locations.…”

Section: Ill-posed Problems In Image Processingmentioning

confidence: 99%

“…The adjoint variable λ is then obtained from the background variable using equations (20) and (21). Last, the incremental variable δX is obtained from the adjoint variable using equations (24) and (25).…”

Section: Incremental Algorithmmentioning

confidence: 99%

Solving ill-posed Image Processing problems using Data Assimilation

Béréziat

Herlin

2010

Numer Algor

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Data Assimilation is a mathematical framework used in environmental sciences to improve forecasts performed by meteorological, oceanographic or air quality simulation models. It aims to solve an evolution equation, describing the temporal dynamics, and an observation equation, linking the state vector and observations. In this article we use this framework to study a class of ill-posed Image Processing problems, usually solved by spatial and temporal regularization techniques. An approach is proposed to convert an ill-posed Image Processing problem in terms of a Data Assimilation system, solved by a 4D-Var method. This is illustrated by the estimation of optical flow from a noisy image sequence, with the dynamic model ensuring the temporal regularity of the result. The innovation of the paper concerns first, the extensive description of the tasks to be achieved for going from an image processing problem to a data assimilation description; second, the theoretical analysis of the covariance matrices involved in the algorithm; and third a specific discretisation scheme ensuring the stability of computation for the application on optical flow estimation.

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Inverse Problem Theory and Methods for Model Parameter Estimation

Cited by 5,598 publications

References 0 publications

Deriving 3-D Time-Series Ground Deformations Induced by Underground Fluid Flows with InSAR: Case Study of Sebei Gas Fields, China

Deriving 3-D Time-Series Ground Deformations Induced by Underground Fluid Flows with InSAR: Case Study of Sebei Gas Fields, China

Earthquake relocation for North-Western Greece using 3D crustal model; method comparison and seismotectonic interpretation.

Solving ill-posed Image Processing problems using Data Assimilation

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