Comparison of frequency and time-domain objective functions for borehole stations inverse problem

Florent de Martin (1, 2)

1 BRGM - Bureau de Recherches Géologiques et Minières (BRGM)
2 MSSMat - Laboratoire de mécanique des sols, structures et matériaux

This paper compares the use of frequency and time-domain objective function for the inversion of the soil structure using borehole station data. It is shown that the length of the cosine-shaped window used to taper the time history to be transformed by the Fast Fourier Transform influences the global shape of the spectral ratios (i.e., both frequency and amplitude of the resonant frequencies of the soil column are affected by the length of the cosine-shaped window). Consequently, the inversions using frequency-domain objective function are distorted by the length of the cosine-shaped windows that is generally chosen arbitrarily between 15 and 50% of the length of the S-wave portion. In order to avoid this effect, this paper introduces a time-domain objective function that computes the integrated residual between a simulated time history and the raw observation. The results show that the match of the simulated time histories with the observation is better when the time-domain objective function is used.

Domains: Other

Florent de Martin. Comparison of frequency and time-domain objective functions for borehole stations inverse problem. 5th International Conference on Earthquake and Geotechnical Engineering, Jan 2011, Santiago, Chile. ⟨hal-00560542⟩