Complete Waveform Inversion Approach To Seismic Surface Waves And Adjoint Active Surfaces

Abstract

The idea to exploit the dispersive mechanism of surface waves as a probing tool
for investigating subsurface structure was introduced about 30 years ago, and after-
wards a very intense research field has developed. Currently many methods known
generally as Surface Wave Methods exist, and are well established, most of them as-
suming layered or depth dependent ground models. In most cases the parallel layer
assumption is correct because the soil structure is expected to negligibly depart from
a layered structure at a typical surface testing scale for engineering and geotechnical
purposes however to exploit the amount of information achievable, it is necessary
to extend the research, relaxing at least one of the underlying model assumptions.
Indeed in classical SWM’s, surface waves are assumed to be Rayleigh waves, this
means that a parallel layered model has been implicitly assumed. As a consequence
search for a soil model geometry other than the assumed one can only result in slight
perturbations. The only possible deduction is that overcoming limitations of layered
models requires to exploit P and S waves which are indeed general solutions of the
elastodynamic problem. Geometry can then be retrived by a complete waveform
inversion based on a forward model capable of successfully reproducing all of the
features of the displacement field in presence of complex scattering phenomena. In
this research effort an inversion approach has been introduced which exploits the
Boundary Element Method as forward model. Such approach is appealing from a
theoretical point of view and is computationally efficient. Although in the present
work a monochromatic signal traveling in a system constituted by a layer over an
half space was investigated, this method is suitable for any number of layers, and
multi-frequency environments. The boundary element approach can be easily gen-
eralized to three-dimensional modeling; moreover viscoelasticity can be introduced
by the elastic-viscoelastic principle of correspondence. Finally BEM can be easily
implemented for parallel computing architecture. Synthetic cases of high and low
impedance Jump were investigated for typical SWM setups and a first example of
application on real data was performed. Finally an elegant analytic form of the min-
imization flow named Adjoint Active Surfaces was obtained combining Computer
Vision technique of Active surfaces and the Adjoint Field method