Simulated Annealing Inversion: Wavelet Estimation

A wavelet is a convolutional operator between log reflectivity traces and the seismic data. In this package, the wavelet is estimated by matching the log and corresponding seismic segments through the cross and power spectra of both segments (White, 1980).

The uncertainty of the estimation can be analyzed by several factors such as predictability, smooth bandwidth ratio, correlation coefficient etc. The accuracy of the wavelet can be measured by the normalized mean square error (NMSE).

The wavelet estimation can be performed on each well, and their spectral characteristics are analyzed. The package also allows external wavelets to be imported for inversion such as Hampton and Russell wavelet and other wavelets.

Wavelet Estimation diagram

From Left to Right: The estimated wavelet; Log reflectivity; Real seismic trace; Synthetic seismic trace; Error trace. Predictability, bandwidth ratio and NMSE are also estimated.

Wavelet Estimation diagram

A Hampton and Russell wavelet can be imported for inversion.

Wavelet Estimation diagram

Top Left: Estimated wavelet; Top Right: Estimated wavelet of a fixed length; Bottom Left: Amplitude spectrum of the wavelet; Bottom Right: Phase spectrum of the wavelet.