Automated spectral recomposition with application in stratigraphic interpretation |

(1) |

where is the spectrum of a seismic trace, and and are the amplitude and peak frequency of the -th Ricker spectrum component, given as

Thus, the model is a linear combination of Ricker wavelet spectra, which has nonlinear functions and depends on multiple parameters. To estimate the Ricker wavelet spectra, we need both and coefficients. The estimation error is

(3) |

The optimal least-squares estimation requires

(4) |

The goal of separable nonlinear least-squares estimation (Björck, 1996) is to find a global minimizer of the sum of squares of nonlinear functions. The separability aspect comes from solving linear and nonlinear parts separately (Scolnik, 1972). The algorithm we use in this paper is known as the variable projection algorithm (Golub and Pereyra, 1973). It provides solutions for and by exploring the fact that depends on linearly.

Automated spectral recomposition with application in stratigraphic interpretation |

2013-08-19