Summary
Extended waveform inversion overcomes the "local minima" obstacle by adding an additional dimension of freedom to the model. However, one main challenge of this method is the computational intensity. In this abstract, we combine multiscale method with an adaptive approach to reduce the computational cost. In the multiscale strategy, the data and the source function are filtered by low-pass filters with low to high cutoff frequencies. Correspondingly, the space decomposition follows a coarse-to-fine scheme. Instead of using fixed subsurface offset range, in our adaptive approach, the adequate range is dynamically determined by measuring the data fitting at each background velocity step. Results from a synthetic example show a great improvement in computational efficiency while maintaining sufficient offset.
Introduction
Least-squares full waveform inversion provides a way to determine the earth properties based on the comparison of the observed data and predicted data obtained from forwarding modeling (Tarantola, 1984). However, due to its highly nonlinear nature, the objective function of typical least-squares functions appears to possess many stationary points (local minima). Aiming to solve the local minima problem, the extended modeling concept links migration velocity analysis with full waveform inversion (Symes, 2008). The extension of the velocity model to subsurface offsets provides a robust solution to the local minima problem of conventional full waveform inversion (Sun and Symes, 2012; Biondi and Almomin, 2012; Almomin et al., 2012). However, the extended waveform inversion is still a challenging data-fitting procedure. One main challenge is the computational intensity from the introduced additional dimension.
Based on the linearized model of acoustic scattering (Born approximation), the pressure field can be divided into two parts: the reference (incident) pressure field u and the scattered (perturbation) field du. The reference pressure field u only contains direct waves and refracted waves, provided that the background velocity v is smooth or slowly varying, on the scale of wave length. The perturbed field depends linearly on the velocity perturbation d v, which is presumed to represent the oscillatory character of Earth structure within wavelength scale. In the constant density acoustic case, these two fields can be expressed as:
