Wave equation tomographyin baseband with phase correction from the first arrival traveltimes

We use the first arrival traveltime to correct the phase distortion in a nonlinear wave equation inversion scheme.This improves the precision of tomographic reconstruction of a velocity structure with large variations and helps solve the ill-posed problem of wave equation inversion.When the variation of the velocity distribution is large,general non-linear wave equation inversions are very ill-posed and for such strong nonlinear we can not obtain a correct inversion.One of main reasons is that the calculated and observed phase of the wavefield differs greatly if the initial model is far from the true model.This leads to highly mismatched phase between the calculated and the observed wave field.This is so-called"Cycle Skipping"problem in the full waveform inversion.The phase mismatch is even more pronounced if a high operating frequency is employed in order to increase resolution.To address this problem,we use the first arrival to"demodulate"the wave field in the frequency domain with a goal of restoring the phase of wave field.Then we minimize an objective function consisting of so called"demodulated"wave field to solve wave equation inversion problem.In this way,we find that the inversion is much improved,and when the velocity perturbation in a complicated model reaches 35%,we can still obtain a good inversion.A computer simulation shows that our method is very robust for acoustical wave inversion with good reconstruction precision.