Full Model Wavenumber Inversion (FMWI)

Abstract

A model of the Earth can be described using a Fourier basis represented by its wavenumber components. In full waveform inversion (FWI), our ultimate objective is to access all the available model wavenumbers in the recorded data that are not already accurately present in the initial velocity model. In inverting for these model wavenumbers, it is important to locate their imprint in the data. To achieve this, I review the relation between the model wavenumber buildup and the inversion process. Specifically, I emphasize a focus on the model wavenumber components and identify their individual influence on the data. Missing the energy for a single vertical low wavenumber from the residual model between the true Marmousi model and some initial linearly increasing velocity model produces a worse least-square fit to the data than the initial model it self where all the residual model wavenumbers are missing. This extreme realization demonstrates the importance of the low model wavenumbers in utilizing the higher wavenumbers, especially those attained in an order dictated by a scattering angle filter. A numerical Marmousi example demonstrates the important role that a scattering angle filter plays in managing the continuation process from low to high model wavenumbers.