Stable Q Analysis on Vertical Seismic Profiling Data

Vertical seismic profiling (VSP) provides a direct observation of seismic waveforms propagating to different depths within the Earth subsurface. Q analysis based on individual waveforms at various depths however suffers from a problem of instability commonly due to fluctuations inherent in the frequency spectrum of each waveform. To improve the stability, it is suggested that, instead of doing Q analysis on individual waveforms, conducting analysis on an integrated observation which considers both frequency and time. The time- (or depth-) frequency domain spectrum is transformed to a 1-D attenuation measurement with respect to a single variable, the product of frequency and time. While this 1-D measurement has higher signal-to-noise ratio than the 2-D spectrum in time-frequency domain, it can also be used to generate a further stabilized compensation function. Then two stable Q analysis methods are implemented by data fitting in least-squares sense to either the attenuation measurement or the data-driven gain function. These two methods are theoretically consistent and practically robust, for conducting Q analysis on field VSP data.