A Comparative Study of Inversion Methods Using Reproduced Low-Frequency Components

Abstract:

Seismic waveform inversion is widely used, and can provide robust results with seismic data. However, in applying waveform inversion techniques to field data there are still many difficulties, such as the local minima problem, the lack of low-frequency components in seismic data, etc. To overcome these problems, several waveform inversion methods have been proposed in order to obtain a velocity model with long-wavelength features. A feature common to these inversion methods is one where they all reproduce low-frequency components, but the actual methods of reproduction of the low-frequencies are different from method to method. In particular, domain (e.g., Laplace transform) and trace (e.g., envelope function, spectral decomposition) transforms are widely utilized to reproduce the enhanced low-frequency components. Since the characteristics of a given reproduced low-frequency component depend on the transformation method, analysis of each method is needed in order to consider its effective application.

In this study, we compared three different inversion methods (Laplace, envelope, and spectrogram inversion) which use the reproduced low-frequency components of seismic data. Firstly, each reproduced seismic data set was analyzed by frequency analysis. It showed that each transformation method reproduces the enhanced low-frequency components. Secondly, we plotted the contours of objective functions using each transformation method. This demonstrated that these inversion methods have a global minimum. Finally, we performed waveform inversion using the modified SEG/EAGE salt A-A’ line model. Numerical examples, with three different inversion methods, indicate that long-wavelength velocity models were generated well. In particular, spectrogram inversion with several decomposed signals recovered the characteristics of subsurface structures more clearly. However, the computational efficiency of the spectrogram inversion was less than that of other approaches.