Quantification of two-dimensional NOE spectra via a combined linear and nonlinear least-squares fit

1994 ◽  
Vol 4 (5) ◽  
pp. 645-652 ◽  
Author(s):  
James W. Brown ◽  
Wray H. Huestis
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Two Dimensional ◽  
Least Squares Fit ◽  
Linear And Nonlinear

scholarly journals Near infrared nadir sounding of vertical column densities: methodology and application to SCIAMACHY

2011 ◽  
Vol 4 (3) ◽  
pp. 3685-3737
Author(s):  
S. Gimeno García ◽  
F. Schreier ◽  
G. Lichtenberg ◽  
S. Slijkhuis
Keyword(s):  
Least Squares ◽  
Near Infrared ◽  
Nonlinear Least Squares ◽  
Retrieval Algorithm ◽  
Atmospheric Gases ◽  
Vertical Column ◽  
Least Squares Fit ◽  
Least Squares Optimization ◽  
Shortwave Infrared ◽  
And Inversion

Abstract. Nadir observations with the shortwave infrared channels of SCIAMACHY onboard the ENVISAT satellite can be used to derive information on atmospheric gases such as CO, CH4, N2O, CO2, and H2O. For the operational level 1b–2 processing of SCIAMACHY data a new retrieval code BIRRA (Beer InfraRed Retrieval Algorithm) has been developed: BIRRA performs a nonlinear least squares fit of the measured radiance, where molecular concentration vertical profiles are scaled to fit the observed data. Here we present the forward modeling (radiative transfer) and inversion (least squares optimization) fundamentals of the code along with the further processing steps required to generate higher level products such as global distributions and time series. Moreover, various aspects of level 1 (observed spectra) and auxiliary input data relevant for successful retrievals are discussed. BIRRA is currently used for operational analysis of carbon monoxide vertical column densities from SCIAMACHY channel 8 observations, and is being prepared for methane retrievals using channel 6 spectra. A set of representative CO retrievals and first CH4 results are presented to demonstrate BIRRA's capabilities.

Molecular Parameters for the a3Πu and b3Σg− States in C2

1975 ◽  
Vol 53 (3) ◽  
pp. 299-302 ◽  
Author(s):  
L. Veseth
Keyword(s):  
Least Squares ◽  
Electronic Spectra ◽  
Nonlinear Least Squares ◽  
Experimental Information ◽  
Present Approach ◽  
Energy Separation ◽  
Molecular Parameters ◽  
Triplet Splitting ◽  
Least Squares Fit

Molecular parameters for the a3Πu and b3Σg− states in C2 (Ballik–Ramsay system) are determined by a nonlinear least squares fit directly to the observed wavelengths. No satellite lines are observed in the electronic spectra of C2, and the influence of nuclear statistics yields further restrictions with regard to observable lines. The present approach, however, yields accurate values of the various triplet splitting and Λ-doubling parameters in spite of this lack of experimental information. Finally a refined value of the triplet–singlet energy separation is obtained.

Translation and Development in Two Dimensional Fields with Special Reference to Pressure Variations

1948 ◽  
Vol 1 (4) ◽  
pp. 412
Author(s):  
RW James
Keyword(s):  
Special Reference ◽  
Least Squares ◽  
Singular Points ◽  
Rate Of Change ◽  
Special Importance ◽  
Two Dimensional ◽  
Practical Result ◽  
Weighting Factors ◽  
Least Squares Fit

In previous studies of translation of field entities attention has been focused on singular points and lines of the field, with the result that the complementary concept of development in the field has been left either not at all, or quite arbitrarily, defined. By determining the least-squares fit to the rate of change of the entity throughout the field, rigid and unique definitions are derived of both the translation and rotation of the system of isolines of the entity, and also of the local and total development in the field. The practical result is to derive a system of weighting factors for the translation of elements of the field, and to stress the special importance of those regions where the gradient of the entity is greatest. In meteorology this means that the movement of pressure-systems is dominated by that of the regions of strongest wind. Comparison is made with earlier results, and the question of the consistent motion of coexistent fields (e.g. pressure and temperature) is discussed.

Automated spectral recomposition with application in stratigraphic interpretation

2013 ◽  
Vol 1 (1) ◽  
pp. SA109-SA116 ◽  
Author(s):  
Yihua Cai ◽  
Sergey Fomel ◽  
Hongliu Zeng
Keyword(s):  
Least Squares ◽  
Frequency Domain ◽  
Seismic Response ◽  
Cross Sections ◽  
Reservoir Characterization ◽  
Nonlinear Least Squares ◽  
Significant Frequency ◽  
Signal Parameters ◽  
Frequency Components ◽  
Linear And Nonlinear

Analyzing seismic attributes in the frequency domain is helpful for reservoir characterization. To analyze the reservoir interval of interest in detail, it is important to capture the seismic response at each frequency subset. Spectral recomposition can be used to extract significant components from the seismic spectrum. We propose a separable nonlinear least-squares algorithm for spectral recomposition, which estimates linear and nonlinear parts automatically in separate steps. Our approach is applied to estimate fundamental signal parameters, peak frequencies, and amplitudes, with which the seismic spectrum can be reconstructed. Automated spectral recomposition helps us visualize frequency-dependent geologic features on cross sections and time slices by extracting significant frequency components. Spectral recomposition can also indicate how frequency contents attenuate with time.

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