Application of weighted early-arrival waveform inversion to shallow land data

• We exactly derive and implement a weighted misfit function for waveform inversion.
• In theory, we show the misfit function focuses on phase match more than amplitudes.
• A synthetic and land data examples validate the advantage of the misfit function.

Seismic imaging of deep land targets is usually difficult since the near-surface velocities are not accurately estimated. Recent studies have shown that inverting traces weighted by the energy of the early-arrivals can improve the accuracy of estimating shallow velocities. In this work, it is explained by showing that the associated misfit gradient function tends to be sensitive to the kinetics of wave propagation and insensitive to the dynamics. A synthetic example verifies the theoretical predictions and shows that the effects of noise and unpredicted amplitude variations in the inversion are reduced using this weighted early arrival waveform inversion (WEWI). We also apply this method to a 2D land data set for estimating the near-surface velocity distribution. The reverse time migration images suggest that, compared to the tomogram inverted directly from the early arrival waveforms, the WEWI tomogram provides a more convincing velocity model and more focused reflections in the deeper part of the image.