Journal ArticleDOI
Generalized Nonlinear Inverse Problems Solved Using the Least Squares Criterion
Albert Tarantola,Bernard Valette +1 more
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In this article, a general definition of the nonlinear least squares inverse problem is given, where the form of the theoretical relationship between data and unknowns may be general (in particular, nonlinear integrodierentia l equations).Abstract:
We attempt to give a general definition of the nonlinear least squares inverse problem. First, we examine the discrete problem (finite number of data and unknowns), setting the problem in its fully nonlinear form. Second, we examine the general case where some data and/or unknowns may be functions of a continuous variable and where the form of the theoretical relationship between data and unknowns may be general (in particular, nonlinear integrodierentia l equations). As particular cases of our nonlinear algorithm we find linear solutions well known in geophysics, like Jackson’s (1979) solution for discrete problems or Backus and Gilbert’s (1970) a solution for continuous problems.read more
Citations
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Origin of Pyroxenite–Peridotite Veined Mantle by Refertilization Reactions: Evidence from the Ronda Peridotite (Southern Spain)
TL;DR: In this paper, a major and trace element and numerical modeling study of a layered outcrop of group C pyroxenite near the locality of Tolox aimed at constraining the origin of these pyroxensites after host peridotites by pervasive pyroxene-producing, refertilization melt^ rock reactions is presented.
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Inverse modeling of the global CO cycle: 1. Inversion of CO mixing ratios
TL;DR: In this paper, a three-dimensional modeling study on atmospheric carbon monoxide is presented, based on the TM2 model, where a Bayesian inverse technique is applied to optimize the agreement between model and data, including a priori source information as regularization term.
Journal ArticleDOI
Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion
TL;DR: In this paper, the quadratic Wasserstein metric is used to measure amplitude differences and global phase shifts, which helps to avoid cycle-skipping issues in full waveform inversion.
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Seismic structure of the upper mantle in a central Pacific corridor
TL;DR: In this article, the seismic structure of the Tonga-Hawaii corridor has been investigated by combining two data sets: Revenaugh and Jordan's reflectivity profile from ScS reverberations, which provides travel times to and impedance contrasts across the major mantle discontinuities, and 1500 new observations of frequency-dependent phase delays for the three-component S, SS, and SSS body waves and the R1 and G1 surface waves, which constrain the velocity structure within this layered framework.
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Thermal convection in a volumetrically heated, infinite Prandtl number fluid with strongly temperature‐dependent viscosity: Implications for planetary thermal evolution
O. Grasset,E. M. Parmentier +1 more
Abstract: Parameterized models of the thermal evolution of planets are usually based on the assumption that the lithosphere-convecting mantle boundary can be defined by an isotherm at a temperature below which viscosity is infinite on geologic timescales. Recent experimental results argue against this assumption. We have investigated both the definition of the lithosphere-convecting mantle boundary and the power law relation describing convecting heat transfer, based on numerical experiments of thermal convection in a volumetrically heated fluid with temperature-dependent viscosity. Other recent studies have treated only the heating from below, but volumetric heating is likely to be the dominant mode of heating in planetary mantles, either as a consequence of radioactive heating or as a proxy for secular cooling. Convection can occur either in the whole box or be located under a stagnant lid. In the lid regime, convection is driven by a temperature contrast depending on the rheology of the fluid and the interior temperature. This result, in agreement with experimental studies, indicates that boundary between the stagnant lid and the convecting layer (similar to the lithosphere-convecting mantle boundary) cannot be defined as a fixed isotherm. During thermal evolution of planets, the viscosity contrast in the convecting mantle remains constant, not the temperature at the bottom of the lithosphere. We present an example showing that the evolution of planets is strongly dependent on the criterion chosen to define the lithosphere-convecting mantle boundary. For reasonable values of the activation energy for thermally activated creep, the temperature defining the lithosphere-convecting mantle boundary, the mantle temperature, and the thickness of the lithosphere could be larger than expected from previous models which treat the base of the lithosphere as a fixed isotherm.
References
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Book
Linear statistical inference and its applications
TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
Journal ArticleDOI
Linear Statistical Inference and Its Applications.
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Uniqueness in the Inversion of Inaccurate Gross Earth Data
George E. Backus,Freeman Gilbert +1 more
TL;DR: In this article, it was shown that a given set G of measured gross Earth data permits such a construction of localized averages, and if so, how to find the shortest length scale over which G gives a local average structure at a particular depth if the variance of the error in computing that local average from G is to be less than a specified amount.
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The general linear inverse problem - Implication of surface waves and free oscillations for earth structure.
TL;DR: In this paper, the discrete general linear inverse problem is reduced to a set of m equations in n unknowns and a linear combination of the eigenvectors of the coefficient matrix can be used to determine parameter resolution and information distribution among the observations.