Determination of the damping ratio by multi-channel spectral analysis of seismic downhole data

Abstract

Soil dynamic parameters such as shear wave velocity and damping ratio are of major interest in earthquake engineering. While the shear wave velocity, directly linked to the shear modulus, can be determined by a number of laboratory and in-situ tests with satisfying accuracy the damping ratio is much more difficult to obtain. Especially the results of in-situ experiments show often large variations. This is in general due to the troublesome determination of precise signal amplitudes whether in time or frequency domain related with these techniques.The paper presented comes back to a relationship between attenuation and velocity dispersion of body waves which replaces the measurement of the amplitude characteristics of seismic signals by a frequency dependent velocity function. The implementation of this method has previously shown to be difficult because of the very small levels of dispersion observed in seismic data. Our approach aims to overcome the problem by applying a multi-channel spectral analysis which is widely used in surface wave testing to calculate a velocity dispersion. Multi-channel measurements have shown to be more tolerant to erroneous phase characteristics of single seismic traces than the more common two station measurements.The velocity dispersion curve is extracted from a phase velocity–frequency spectrum and the damping ratio is calculated by fitting a theoretical dispersion curve to the extracted curve. The method is demonstrated on correlated data of a seismic downhole test performed using a S-wave vibrator source. The obtained results show a reasonable agreement with damping ratios found in the literature for similar soils.