Phase inversion of seismic data with estimation of source phase: Synthetic examples

We propose a new and reliable velocity inversion technique for the seismic data. Our algorithm models the acoustic wave equation, exploiting the frequency domain finite element modeling to calculate the Jacobian of the phase of the seismic data with respect to the earth model parameter such as a velocity. Geophysicists have had difficulties when implementing the waveform, inversion in the source estimation of the seismic data. We solve the issue of the source estimation by adding the step of recovering the phase information of the source wavelet into our algorithm. Our algorithm implements an iterative inversion of the source phase from the objective function of the source with respect to phase by using the classical full Newton method. The inversion technique in the category of 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 because of 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.