Elastic Full Waveform Inversion with envelope based misfit function

The lack of low-frequency information in seismic data leads to difficulty in obtaining long wavelength background model for Full Waveform Inversion (FWI). In addition, traditional FWI with acoustic wave equation is not suitable in describing wave propagations to accommodate surface and converted waves. In this paper, based on the elastic wave equations, we develop an envelope-based misfit function for elastic FWI to estimate the long wavelength components of two elastic parameters: P-wave and S-wave. The inversion employs a staggered-grid finite difference solution of the 2-D elastic wave equation in the time domain, allowing accurate simulation of all possible waves in elastic media. A synthetic example based on the Marmousi II model illustrates that the envelope-based elastic FWI method can provide an adequately accurate initial model for the traditional FWI approach even when the initial models are far from the true models and low frequency data are limited.