A comparison between Laplace domain and frequency domain methods for inverting seismic waveforms

We compared the ability of full waveform inversion to recover background velocity models from data containing no low-frequency information using the frequency and Laplace domains. Low-frequency information is crucial for recovering background velocity when using frequency-domain waveform inversions. However, the dearth of low-frequency information in field data makes frequency-domain inversion impractical without accurate starting velocity models. Instead, by performing waveform inversion in the Laplace domain, one can recover a smooth velocity model that can be used for either migration or for subsequent frequency-domain inversion as an accurate initial velocity model. The Laplace-transformed wavefield can be thought of as the zero-frequency component of a damped wavefield over a range of damping constants. In this paper, we compare results obtained from both frequency-and Laplace-domain inversions and confirm that the Laplace-domain inversion can be used to recover background velocity from real data without low-frequency information. We also demonstrate that the Laplace-domain inversion can provide the frequency-domain inversion with smooth initial velocity models for better inversion results.