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William Menke - One of the best experts on this subject based on the ideXlab platform.
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Continuous Inverse Theory and Tomography
Geophysical Data Analysis: Discrete Inverse Theory, 2020Co-Authors: William MenkeAbstract:This chapter extends the discrete Inverse Theory that is the main focus of this book to continuous problems. Localized averages are shown to be particularly useful in continuous problems, and the Backus-Gilbert techniques for developing generalized Inverses with localized resolution are extended to the continuous case. The conversion of continuous problems to discrete problems, accomplished earlier in the book in an ad hoc fashion, is examined in a more systematic way. Attention is then turned to problems in which the data are sufficiently numerous that they can be considered a continuous function. The tomography problem is one of these, and the simplest straight-line ray version, Radon's problem, is derived and solved. Attention is then turned to generalizing the quantities and solution techniques of discrete Inverse to the continuous case. Here, the vector is replaced with the function and the matrix with the linear operator. A key quantity, analogous to the transpose of a matrix, is the adjoint of the linear operator. It is at the heart of so-called adjoint methods of deriving the Frechet derivative of data with respect to the model, the continuous analog of the data kernel. Several useful Frechet derivatives are derived, including one relevant to the case where the data and model function are related indirectly, through a differential equation.
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Applications of Inverse Theory to Solid Earth Geophysics
Geophysical Data Analysis: Discrete Inverse Theory, 2020Co-Authors: William MenkeAbstract:This chapter is a survey of the current state of Inverse Theory in solid earth geophysics. Topics that are surveyed include earthquake location methods (including double-difference methods), travel time tomography, earthquake moment tensor inversion, waveform tomography (including the so-called banana-doughnut kernels), free oscillation and surface wave inversions, surface wave tomography, attenuation tomography, signal correlation, tectonic plate motions and geodesy, gravity and geomagnetism, and electromagnetic induction (including the magnetotelluric method). The discussion references an extensive bibliography of classic articles that provide further details.
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Chapter 14 – Appendices
Geophysical Data Analysis: Discrete Inverse Theory, 2020Co-Authors: William MenkeAbstract:This chapter consists of two short appendices that provide methodological details. The first provides a geometrical derivation of Lagrange multipliers, a technique used in the book to implement minimization of a function subject to equality constraints. The second discusses how the formulas of probability Theory and Inverse Theory can be generalized to handle complex numbers. While the most typical applications of Inverse Theory arise in cases where the data are purely real, complex data are occasionally encountered, especially in spectral analysis.
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geophysical data analysis discrete Inverse Theory third edition matlab edition international geophysics series by william menke
2012Co-Authors: William MenkeAbstract:Geophysical Data Analysis Discrete Inverse Theory Geophysical Data Analysis Discrete Inverse Theory MATLAB Edition 3e by William Menke http://alt.math.undergrad.narkive.com/0WROv6Jb/huge-collection-of-new-solution-manuals-2012 Geophysical Data Analysis: Discrete Inverse Theory, Third Edition: Matlab Edition International Geophysics Discrete Inverse Theory, Matlab Edition. Menke http://www.abebooks.com/book-search/isbn/9780123971609/
J. M. Picone - One of the best experts on this subject based on the ideXlab platform.
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Discrete Inverse Theory for 834‐Å ionospheric remote sensing
Radio Science, 1997Co-Authors: J. M. Picone, R. R. Meier, O. A. Kelley, D. J. Melendez-alvira, K. F. Dymond, R. P. Mccoy, Michael J. BuonsantoAbstract:In the near future a number of global, multiyear, satellite-borne ultraviolet remote sensing missions will scan or image the limb of the Earth to measure the O+ concentration within the ionospheric F layer. On the day side we will use discrete Inverse Theory (DIT) to retrieve vertical profiles of the O+ number density from measurements of the 834-A airglow. Here we describe the theoretical foundations and the components of the retrieval code, which computes both a maximum likelihood solution and the associated covariance matrix. New results include enhancement of the DIT formalism to distinguish between random and nonrandom (“systematic”) errors and comparisons of Millstone Hill incoherent scatter radar (ISR) data with generalized Chapman-type representations of the O+ density profile. Of the candidates, the Chapman-type profile with a constant-gradient scale height provides the best fits to the ISR data.
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Discrete Inverse Theory for 834-Å ionospheric remote sensing
Radio Science, 1997Co-Authors: J. M. Picone, R. R. Meier, O. A. Kelley, D. J. Melendez-alvira, K. F. Dymond, R. P. Mccoy, Michael J. BuonsantoAbstract:In the near future a number of global, multiyear, satellite-borne ultraviolet remote sensing missions will scan or image the limb of the Earth to measure the O+ concentration within the ionospheric F layer. On the day side we will use discrete Inverse Theory (DIT) to retrieve vertical profiles of the O+ number density from measurements of the 834-Å airglow. Here we describe the theoretical foundations and the components of the retrieval code, which computes both a maximum likelihood solution and the associated covariance matrix. New results include enhancement of the DIT formalism to distinguish between random and nonrandom (“systematic”) errors and comparisons of Millstone Hill incoherent scatter radar (ISR) data with generalized Chapman-type representations of the O+ density profile. Of the candidates, the Chapman-type profile with a constant-gradient scale height provides the best fits to the ISR data.
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Calculation of the Ionospheric O(+) Concentration from O II 834 A Airglow Using Discrete Inverse Theory.
1995Co-Authors: J. M. Picone, R. R. Meier, K. F. Dymond, R. P. Mccoy, O. A. KelleyAbstract:Abstract : Discrete Inverse Theory (DIT) forms the basis of new techniques for extracting dayside O(+) number density profiles from the 834 A airglow, as measured by a limb-scanning system on an orbiting satellite. Our tests of this method assume observations from an altitude of 850 km with scans from 10 deg to 26.5 deg below horizontal, consistent with future multiyear missions. The retrieval code computes an iterative, maximum likelihood solution by comparing observations to estimates calculated with a new forward model. The model includes multiple resonant scattering and pure absorption. To generate synthetic data for tests, we represent the true O(+) distribution as a Chapman layer and compute an intensity profile with the forward model, adding simulated noise. We present detailed studies of convergence properties of the retrieval techniques and of uncertainties in the retrieved parameters. For this baseline (Chapman layer) case, the method is robust, converging to an accurate solution for a wide variation in synthetic data. We include a brief preview of recent studies showing the following: (1) for future missions, the DIT method can correctly distinguish between distinctly different Chapman layers that produce nearly identical intensity profiles and (2) the retrieval of an additional parameter that scales the model intensity profile can compensate for inaccuracies in the instrument sensitivity or in the magnitude of the initial volume excitation rate. (AN)
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Retrieval of absolute thermospheric concentrations from the far UV dayglow: An application of discrete Inverse Theory
Journal of Geophysical Research, 1994Co-Authors: R. R. Meier, J. M. PiconeAbstract:The photoelectron-excited far ultraviolet dayglow provides a means for remote sensing a N{sub 2}, O, O{sub 2}, and temperature in the terrestrial thermosphere. This paper describes a model based on the maximum likelihood method of nonlinear discrete Inverse Theory, which extracts information on the state of the thermosphere from limb scans of the dayglow. The authors show that concentrations between about 150 and (at least) 350 km can be retrieved to a high degree of accuracy and precision, independent of instrument absolute calibration. Also, the retrieved concentrations are not strongly sensitive to errors in the photoelectron excitation cross sections. The model will allow the routine development of climatological databases on the thermosphere from satellite remote sensing missions. 35 refs., 8 figs., 1 tab.
Dimitri Basov - One of the best experts on this subject based on the ideXlab platform.
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Extracting the electron-boson spectral function a 2 FÑvÖ from infrared and photoemission data using Inverse Theory
Environmental Science & Technology, 2020Co-Authors: Sasa Dordevic, Christopher C. Homes, J. J. Tu, Tonica Valla, Myron Strongin, Peter D. Johnson, G. D. Gu, Dimitri BasovAbstract:We present a method for extracting the electron-boson spectral function a 2 Fsvd from infrared and photoemission data. This procedure is based on Inverse Theory and will be shown to be superior to previous techniques. Numerical implementation of the algorithm is presented in detail and then used to accurately determine the doping and temperature dependence of the spectral function in several families of high-Tc superconductors. Principal limitations of extracting a 2 Fsvd from experimental data will be pointed out. We directly compare the IR and angular-resolved photoemission spectroscopy a 2 Fsvd and discuss the resonance structure in the spectra in terms of existing theoretical models.
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extracting the electron boson spectral function α 2 f ω from infrared and photoemission data using Inverse Theory
Physical Review B, 2005Co-Authors: Sasa Dordevic, Christopher C. Homes, J. J. Tu, Tonica Valla, Myron Strongin, Peter D. Johnson, Genda Gu, Dimitri BasovAbstract:We present a method for extracting the electron-boson spectral function ${\ensuremath{\alpha}}^{2}F(\ensuremath{\omega})$ from infrared and photoemission data. This procedure is based on Inverse Theory and will be shown to be superior to previous techniques. Numerical implementation of the algorithm is presented in detail and then used to accurately determine the doping and temperature dependence of the spectral function in several families of high-${T}_{c}$ superconductors. Principal limitations of extracting ${\ensuremath{\alpha}}^{2}F(\ensuremath{\omega})$ from experimental data will be pointed out. We directly compare the IR and angular-resolved photoemission spectroscopy ${\ensuremath{\alpha}}^{2}F(\ensuremath{\omega})$ and discuss the resonance structure in the spectra in terms of existing theoretical models.
Michael J. Buonsanto - One of the best experts on this subject based on the ideXlab platform.
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Discrete Inverse Theory for 834‐Å ionospheric remote sensing
Radio Science, 1997Co-Authors: J. M. Picone, R. R. Meier, O. A. Kelley, D. J. Melendez-alvira, K. F. Dymond, R. P. Mccoy, Michael J. BuonsantoAbstract:In the near future a number of global, multiyear, satellite-borne ultraviolet remote sensing missions will scan or image the limb of the Earth to measure the O+ concentration within the ionospheric F layer. On the day side we will use discrete Inverse Theory (DIT) to retrieve vertical profiles of the O+ number density from measurements of the 834-A airglow. Here we describe the theoretical foundations and the components of the retrieval code, which computes both a maximum likelihood solution and the associated covariance matrix. New results include enhancement of the DIT formalism to distinguish between random and nonrandom (“systematic”) errors and comparisons of Millstone Hill incoherent scatter radar (ISR) data with generalized Chapman-type representations of the O+ density profile. Of the candidates, the Chapman-type profile with a constant-gradient scale height provides the best fits to the ISR data.
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Discrete Inverse Theory for 834-Å ionospheric remote sensing
Radio Science, 1997Co-Authors: J. M. Picone, R. R. Meier, O. A. Kelley, D. J. Melendez-alvira, K. F. Dymond, R. P. Mccoy, Michael J. BuonsantoAbstract:In the near future a number of global, multiyear, satellite-borne ultraviolet remote sensing missions will scan or image the limb of the Earth to measure the O+ concentration within the ionospheric F layer. On the day side we will use discrete Inverse Theory (DIT) to retrieve vertical profiles of the O+ number density from measurements of the 834-Å airglow. Here we describe the theoretical foundations and the components of the retrieval code, which computes both a maximum likelihood solution and the associated covariance matrix. New results include enhancement of the DIT formalism to distinguish between random and nonrandom (“systematic”) errors and comparisons of Millstone Hill incoherent scatter radar (ISR) data with generalized Chapman-type representations of the O+ density profile. Of the candidates, the Chapman-type profile with a constant-gradient scale height provides the best fits to the ISR data.
R. R. Meier - One of the best experts on this subject based on the ideXlab platform.
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Discrete Inverse Theory for 834‐Å ionospheric remote sensing
Radio Science, 1997Co-Authors: J. M. Picone, R. R. Meier, O. A. Kelley, D. J. Melendez-alvira, K. F. Dymond, R. P. Mccoy, Michael J. BuonsantoAbstract:In the near future a number of global, multiyear, satellite-borne ultraviolet remote sensing missions will scan or image the limb of the Earth to measure the O+ concentration within the ionospheric F layer. On the day side we will use discrete Inverse Theory (DIT) to retrieve vertical profiles of the O+ number density from measurements of the 834-A airglow. Here we describe the theoretical foundations and the components of the retrieval code, which computes both a maximum likelihood solution and the associated covariance matrix. New results include enhancement of the DIT formalism to distinguish between random and nonrandom (“systematic”) errors and comparisons of Millstone Hill incoherent scatter radar (ISR) data with generalized Chapman-type representations of the O+ density profile. Of the candidates, the Chapman-type profile with a constant-gradient scale height provides the best fits to the ISR data.
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Discrete Inverse Theory for 834-Å ionospheric remote sensing
Radio Science, 1997Co-Authors: J. M. Picone, R. R. Meier, O. A. Kelley, D. J. Melendez-alvira, K. F. Dymond, R. P. Mccoy, Michael J. BuonsantoAbstract:In the near future a number of global, multiyear, satellite-borne ultraviolet remote sensing missions will scan or image the limb of the Earth to measure the O+ concentration within the ionospheric F layer. On the day side we will use discrete Inverse Theory (DIT) to retrieve vertical profiles of the O+ number density from measurements of the 834-Å airglow. Here we describe the theoretical foundations and the components of the retrieval code, which computes both a maximum likelihood solution and the associated covariance matrix. New results include enhancement of the DIT formalism to distinguish between random and nonrandom (“systematic”) errors and comparisons of Millstone Hill incoherent scatter radar (ISR) data with generalized Chapman-type representations of the O+ density profile. Of the candidates, the Chapman-type profile with a constant-gradient scale height provides the best fits to the ISR data.
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Calculation of the Ionospheric O(+) Concentration from O II 834 A Airglow Using Discrete Inverse Theory.
1995Co-Authors: J. M. Picone, R. R. Meier, K. F. Dymond, R. P. Mccoy, O. A. KelleyAbstract:Abstract : Discrete Inverse Theory (DIT) forms the basis of new techniques for extracting dayside O(+) number density profiles from the 834 A airglow, as measured by a limb-scanning system on an orbiting satellite. Our tests of this method assume observations from an altitude of 850 km with scans from 10 deg to 26.5 deg below horizontal, consistent with future multiyear missions. The retrieval code computes an iterative, maximum likelihood solution by comparing observations to estimates calculated with a new forward model. The model includes multiple resonant scattering and pure absorption. To generate synthetic data for tests, we represent the true O(+) distribution as a Chapman layer and compute an intensity profile with the forward model, adding simulated noise. We present detailed studies of convergence properties of the retrieval techniques and of uncertainties in the retrieved parameters. For this baseline (Chapman layer) case, the method is robust, converging to an accurate solution for a wide variation in synthetic data. We include a brief preview of recent studies showing the following: (1) for future missions, the DIT method can correctly distinguish between distinctly different Chapman layers that produce nearly identical intensity profiles and (2) the retrieval of an additional parameter that scales the model intensity profile can compensate for inaccuracies in the instrument sensitivity or in the magnitude of the initial volume excitation rate. (AN)
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Retrieval of absolute thermospheric concentrations from the far UV dayglow: An application of discrete Inverse Theory
Journal of Geophysical Research, 1994Co-Authors: R. R. Meier, J. M. PiconeAbstract:The photoelectron-excited far ultraviolet dayglow provides a means for remote sensing a N{sub 2}, O, O{sub 2}, and temperature in the terrestrial thermosphere. This paper describes a model based on the maximum likelihood method of nonlinear discrete Inverse Theory, which extracts information on the state of the thermosphere from limb scans of the dayglow. The authors show that concentrations between about 150 and (at least) 350 km can be retrieved to a high degree of accuracy and precision, independent of instrument absolute calibration. Also, the retrieved concentrations are not strongly sensitive to errors in the photoelectron excitation cross sections. The model will allow the routine development of climatological databases on the thermosphere from satellite remote sensing missions. 35 refs., 8 figs., 1 tab.
