Frequency-dependent wave equation traveltime inversion

We demonstrate the cross-correlation based traveltime residuals estimated from band limited seismic data vary according to the components in the frequency band, and propose a method to invert such frequency dependent traveltime residuals for velocity inversion. The proposed inversion algorithm is based on the wave equation and is referred to as FWT (frequency dependent wave equation traveltime inversion). In the proposed method, we start the inversion using cross-correlation based traveltime residuals estimated within low frequency data, followed by the inversion at higher frequencies. The effectiveness and performance of the FWT method is demonstrated by using a synthetic cross-well dataset. The numerical results show that the FWT yields improved results compared to those resulted from the conventional wave equation traveltime inversion (WT) approach, and FWT is more suitable to be the initial velocity model for the subsequent high resolution velocity inversion, e.g., full waveform inversion.