Improve the resolution of vertical seismic profile with a traveltime-varying inverse Q filtering

Seismic waves propagating in absorbing medium suffer from attenuation which increases with the increasing of frequency and travel time. The loss of high frequencies degrades the seismic resolution. Inverse Q filtering can remove the attenuation. The travelling paths of vertical seismic profile(VSP) waves are different from those of surface seismic. The existed inverse Q filtering methods for VSP have deficiencies as following:1.Directly applying the inverse Q filtering methods of surface seismic to VSP often brings inexact results. 2.The efficiency of the methods in frequency domain is quite low because of the long inverse operator. 3.The methods in time domain fail to give accurate results at later time. In order to improve the resolution of VSP data, we derive a traveltime-varying inverse Q filter for VSP. Firstly, we setup the VSP time domain forward Q matrix by adding an correcting factor which is a function of traveltime; Secondly, using banded matrix solver we solve the inverse Q filter directly from the corrected Q modeling equation in time domain. Both numerical synthetic VSP data and field VSP data show that the traveltime-varying inverse Q filter can not only improve the S/N ratio, enhance the resolution of VSP data, but also gain 30 times improvement in computational efficiency comparable to conventional method.