On the Effects of Geometrical Spreading Corrections for a 2D Full Waveform Inversion of Recorded Shallow Seismic Surface Waves

Abstract

Elastic full waveform inversion (FWI) of shallow seismic surface waves has the potential to reconstruct lateral variations of the shallow subsurface which is important e.g. for geotechnical site characterization. In order to make a 2D full waveform inversion algorithm applicable, shallow seismic field recordings excited by a point source (usually a hammer blow) must be transformed to mimic equivalent wavefields excited by a line source. Waves excited by a point source differ in geometrical spreading, i.e. amplitude decay and phase delay of Pi/4 in the far field from waves excited by a line source. When using the L2 norm as a measure of misfit a correction for the different decay of amplitudes is mandatory but not sufficient to obtain reliable results. In addition the signal phase must also be corrected which can be done by a convolution with 1/sqrt(t) or a Fourier-Bessel-expansion. Both spreading corrections work quite well for surface waves.