The Comparison between Refraction-traveltime Tomography and Laplace-domain Waveform Inversion

Since both refraction-traveltime tomography and Laplace-domain waveform inversion recover long-wavelength velocity structures, both methods are widely used to construct a starting velocity model for full waveform inversion. Unfortunately, the characteristics and theoretical aspects of Laplace-domain waveform inversion have not been studied as fully as those of refraction-traveltime tomography. Accordingly, it has been suggested that Laplace-domain waveform inversion is equivalent to refraction-traveltime tomography. However, Laplace-domain waveform inversion is different from refraction-traveltime tomography in many aspects. From sensitivity images, we can note that the result of refraction-traveltime tomography is significantly affected by anomalies in shallow areas. If we use excessively long offset distances to recover deeper layers, refraction-traveltime tomography fails to delineate not only deep structures but also shallow structures. In Laplace-domain waveform inversion, on the other hand, it is possible to detect the deeper structures using small Laplace damping constants and long offset distances. From the inversion examples using a synthetic BP model, we observe that refraction-traveltime tomography cannot detect the structures in the deep area, while Laplace-domain waveform inversion can successfully recover the deep structures in addition to the shallow structures.