Phase Inversion of Seismic Data With Unknown Source Wavelet : Synthetic Examples

We propose a new and reliable velocity inversion technique of seismic data in this study. Our algorithm models the acoustic wave equation, exploiting a frequency domain finite element modeling technique to calculate the Jacobian of the phase of the seismic data with respect to the earth model parameter such as a velocity. Geophysicists have encountered difficulties when implementing a waveform inversion in the source estimation of the seismic data. We solve the issue of the source estimation, adding the step of recovering the phase information of source wavelet into our algorithm. Our algorithm implements an iterative inversion of the source phase at the time when we calculate the residual error vector from the objective function including the source phase. Waveform inversion requires extracting the reliable low frequency content of seismic data to estimate the low wave number velocity model. It is difficult to acquire the reliable low frequency component of real seismic data due to the band limited characteristic of the source and receivers. In this study, we assume that it is possible to extract the reliable component of low frequency, especially with respect to phase information. Through synthetic numerical examples, we will attempt to demonstrate the feasibility of our method in estimating the correct velocity model for prestack depth migration.