Improving surface-wave group velocity measurements by energy reassignment

Surface waves are increasingly used for shallow seismic surveys-in particular, in acoustic logging, environmental, and engineering applications. These waves are dispersive, and their dispersion curves are used to obtain shear velocity profiles with depth. The main obstacle to their more widespread use is the complexity of the associated data processing and interpretation of the results. Our objective is to show that energy reassignment in the time-frequency domain helps improve the precision of group velocity measurements of surface waves. To show this, full-waveform seismograms with added white noise for a shallow flat-layered earth model are analyzed by classic and reassigned multiple filter analysis (MFA). Classic MFA gives the expected smeared image of the group velocity dispersion curve, while the reassigned curve gives a very well-constrained, narrow dispersion curve. Systematic errors from spectral fall-off are largely corrected by the reassignment procedure. The subsequent inversion of the dispersion curve to obtain the shear-wave velocity with depth is carried out through a procedure combining linearized inversion with a nonlinear Monte Carlo inversion. The diminished uncertainty obtained after reassignment introduces significantly better constraints on the earth model than by inverting the output of classic MFA. The reassignment is finally carried out on data from a shallow seismic survey in northern Belgium, with the aim of determining the shear-wave velocities for seismic risk assessment. The reassignment is very stable in this case as well. The use of reassignment can make dispersion measurements highly automated, thereby facilitating the use of surface waves for shallow surveys.