Multi-objective full waveform inversion in the absence of low frequencies

Least-squares inversion of seismic reflection waveforms can reconstruct remarkably detailed models of the Earth’s subsurface. However, the cycle-skipping associated with the highfrequency waveforms are responsible for spurious local minima in its objective function. Therefore, it is often difficult for descent methods to converge to the true model without starting from an accurate large-scale velocity estimate. To partially overcome this difficulty, we propose to use multiple objective functions for inversion. An additional constraint based on cross-correlation is added to the conventional least-squares (LS) inversion. Observations suggest this will result in a model with an accurate background velocity and reflectivity that corresponds to the global minimum of the least-squares objective function. Optimization of a cross-correlation based function (CC) in the data domain appears to pull the trapped solution out of the local minima associated with the least-squares objective function, and vice versa. Some 2-D numerical tests confirm the validity of the approach in the absence of low temporal data frequencies, starting from a constant initial velocity model