##### Surface-wave inversion for a P-velocity profile with a constant depth gradient of the squared slowness

Authors:
A.V. Ponomarenko, B.M. Kashtan, V.N. Troyan and W.A. Mulder

Journal name: Geophysical Prospecting

Issue: Vol 65, No 4, July 2017 pp. 941 - 955

DOI: 10.1111/1365-2478.12450

Organisations:
Wiley

Language: English

Info: Article, PDF ( 3.18Mb )

Summary:

Surface waves are often used to estimate a near-surface shear-velocity profile. The
inverse problem is solved for the locally one-dimensional problem of a set of homogeneous
horizontal elastic layers. The result is a set of shear velocities, one for each
layer. To obtain a P-wave velocity profile, the P-guided waves should be included in
the inversion scheme. As an alternative to a multi-layered model, we consider a simple
smooth acoustic constant-density velocity model, which has a negative constant vertical
depth gradient of the squared P-wave slowness and is bounded by a free surface
at the top and a homogeneous half-space at the bottom. The exact solution involves
Airy functions and provides an analytical expression for the dispersion equation. If
the vs/vp ratio is sufficiently small, the dispersion curves can be picked from the
seismic data and inverted for the continuous P-wave velocity profile. The potential
advantages of our model are its low computational cost and the fact that the result
can serve as a smooth starting model for full-waveform inversion. For the latter, a
smooth initial model is often preferred over a rough one. We test the inversion approach
on synthetic elastic data computed for a single-layer P-wave model and on
field data, both with a small vs/vp ratio. We find that a single-layer model can recover
either the shallow or deeper part of the profile but not both, when compared with
the result of a multi-layer inversion that we use as a reference. An extension of our
analytic model to two layers above a homogeneous half-space, each with a constant
vertical gradient of the squared P-wave slowness and connected in a continuous manner,
improves the fit of the picked dispersion curves. The resulting profile resembles a
smooth approximation of the multi-layered one but contains, of course, less detail. As
it turns out, our method does not degrade as gracefully as, for instance, diving-wave
tomography, and we can only hope to fit a subset of the dispersion curves. Therefore,
the applicability of the method is limited to cases where the vs/vp ratio is small and
the profile is sufficiently simple. A further extension of the two-layer model to more
layers, each with a constant depth gradient of the squared slowness, might improve
the fit of the modal structure but at an increased cost.

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