scholarly journals Circle fitting by linear and nonlinear least squares

1993 ◽  
Vol 76 (2) ◽  
pp. 381-388 ◽  
Author(s):  
I. D. Coope
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Circle Fitting ◽  
Linear And Nonlinear

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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