(untitled) (Communications in Computational Physics, 2020)
In the contrast source inversion (CSI) method, the contrast sources (equivalent scattering sources) and the contrast (parameter perturbation) are iteratively reconstructed by an alternating optimization scheme. Traditionally integral equation CSI method is formulated for transmission tomography using analytic Green's function in homogeneous background. To extend the method to the case of reflection seismology, in this paper, we use WKBJ method to compute the Green's function of depth dependent background media and the solving method of equations to initialize the contrast source of different frequencies, resulting in an efficient method to invert multi-frequency reflection seismic data – multi-frequency contrast source inversion method (MFCSI). Numerical results for the Marmousi model show that MFCSI method can obtain good results even when low frequency data are missing, in which case the conventional FWI fails.