An IMAP Method for Inversion of Medium Q Factor Using Zero-Offset VSP Data

In the zero-offset vertical seismic profile (VSP), if the data noise is weak, the spectral ratio method (SRM) is considered to be the most reliable and commonly used method for estimating the medium
$Q$
factor. However, due to the possible picking error in the first-arrival time of the downgoing waveform, the estimated
$Q$
value fluctuates, which affects the subsequent attenuation compensation and lithology analysis. In order to overcome this fluctuation, we present an iterative maximum posterior probability (IMAP) method that uses zero-offset VSP data to invert the medium
$Q$
factor. Based on SRM, this method gives the maximum posterior probability (MAP) method for inverting the quality factor
$Q$
, establishes the update formulas of quality factor
$Q$
and travel time difference
$\Delta t$
, and performs alternate iterations on them. Since the prior information of the formation is introduced and
$\Delta t$
is corrected in each iteration, the inversion result can eliminate the fluctuations in the
$Q$
value and velocity caused by the
$\Delta t$
error. Two synthetic experimental examples and one field experiment verify the effectiveness and superiority of the proposed method.