Nonperturbational surface-wave inversion: A Dix-type relation for surface waves
We extend the approach underlying the well-known Dix equation in reflection seismology to surface waves. Within the context of surface wave inversion, the Dix-type relation we derive for surface waves allows accurate depth profiles of shear-wave velocity to be constructed directly from phase velocity data, in contrast to perturbational methods. The depth profiles can subsequently be used as an initial model for nonlinear inversion. We provide examples of the Dix-type relation for under-parameterized and over-parameterized cases. In the under-parameterized case, we use the theory to estimate crustal thickness, crustal shear-wave velocity, and mantle shear-wave velocity across the Western U.S. from phase velocity maps measured at 8-, 20-, and 40-s periods. By adopting a thin-layer formalism and an over-parameterized model, we show how a regularized inversion based on the Dix-type relation yields smooth depth profiles of shear-wave velocity. In the process, we quantitatively demonstrate the depth sensitivity of surface-wave phase velocity as a function of frequency and the accuracy of the Dix-type relation. We apply the over-parameterized approach to a near-surface data set within the frequency band from 5 to 40 Hz and find overall agreement between the inverted model and the result of full nonlinear inversion.
Additional Information© 2015 Society of Exploration Geophysicists. Manuscript received by the Editor 28 December 2014; revised manuscript received 28 April 2015; published online 16 October 2015. The authors wish to thank F.-C. Lin for providing access to the phase velocity maps of the western United States. They also thank assistant editor V. Socco, associate editor G. Tsoflias, P. Dawson, and three anonymous reviewers for their helpful comments.
Published - geo2014-0612.1.pdf